Complement: 0.4 x 0.8 = =.6

Size: px
Start display at page:

Download "Complement: 0.4 x 0.8 = =.6"

Transcription

1 Homework Chapter 5 Name: 1. Use the graph below 1 a) Why is the total area under this curve equal to 1? Rectangle; A = LW A = 1(1) = 1 b) What percent of the observations lie above 0.8? =.2; A = LW A = 1(.2) =.2; 20% c) What percent of the observations lie between 0.25 and 0.75? =.5; A = LW A = 1(.5) =.5; 50% d) What is the mean of this distribution? μ =.5 2. Use the graph below 3 2 a) Verify that the graph is a valid density curve. All on or above horizontal axis; Rectangle + Triangle1(. 8) + 1 (1). 4) = b) The median of this density curve is a point between X = 0.2 and X = 0.4. Explain why. 0 x.2 =.35 and. 4 x.8 =.4;.5 has to be between.2 and.4 c) Find the proportion of observations within each interval i 0.6 < x < 0.8 ii 0 < x < 0.4 iii 0 < x < =.2 1(. 2) =.2 Complement: 0.4 x 0.8 = =.6 Trapezoid: A = 1 (. 2)( ) = ) The sketch below contains three normal curves; think of them as approximating the distribution of exam scores for three different classes. One (call it A) has a mean of 70 and a standard deviation of 5; another (call it B) has a mean of 70 and a standard deviation of 10; the third (call it C) has a mean of 50 and a standard deviation of 10. Identify which is which by labeling each curve with its appropriate letter. A C B

2 4) For each of the following normal curves, identify (as accurately as you can from the graph) the mean and standard deviation of the distribution. μ = 50 σ = 5 μ = 1100 σ = 300 μ = 10 σ = 40 μ = 225 σ = 75 5) Suppose the average height of women collegiate volleyball players is 5 9, with a standard deviation of 2.1. Assume that heights among these players follow a mound-shaped distribution. a) Draw the curve and label it b) According to the empirical rule, about 95% of women collegiate volleyball players have heights between what two values? 64.8 to 73.2 c) What does the empirical rule say about the proportion of players who are between 62.7 inches and 75.3 inches? 99.7% of players are between 62.7 and 75.3 inches tall d) Reasoning from the empirical rule, what is the tallest we would expect a woman collegiate volleyball player to be? 75.3 inches would cover all but.15% e) About what percent of women collegiate volleyball players are taller than 71.1 inches? 16% f) About what percent of women collegiate volleyball players are shorter than 64.8 inches? 2.5% g) Find the percentiles for the following heights: th 50 th 97.5 th th

3 6) Given an approximately normal distribution, N(175, 37). a. Draw a normal curve and label 1, 2, and 3 standard deviations on both sides of the mean. b. What percent of values are within the interval (138, 212)? 68% c. What percent of values are within the interval (101, 249)? 95% d. What percent of values are within the interval (64, 286)? 99.7% e. What percent of values are outside the interval (138, 212)? 32% f. What percent of values are outside the interval (64, 286)? 0.3% ) The incubation time for Rhode Island Red chicks is normally distributed with a mean 21 days and standard deviation approximately 1 day. a. Draw a normal curve and label 1, 2, and 3 standard deviations on both sides of the mean If 1000 eggs are being incubated, how many chicks do we expect will hatch in each of the following situations? b. In 19 to 23 days c. In 18 days or more d. In 22 days or less 95% of 1000 = % of 1000 = % of 1000 = 840 8) Use the table of standard normal probabilities to determine the proportion of the normal curve that falls within: a. one standard deviation of its mean (in other words, between z-scores of 1 and 1) =.6826 b. two standard deviations from the mean =.9544 c. three standard deviations from the mean =.9974 d. Compare these values to the values obtained from the empirical rule. They are all very close to the proportions described by the Empirical Rule.

4 9) Use the table of standard normal probabilities to determine the proportion of observations from a standard normal distribution that satisfies each of the following statements. For each, sketch a standard normal curve and shade the area under the curve that is the answer. a. z < 2.85 b. z > 2.85 c. z > d < z < 2.85 P(z < 2.85) =.9978 P(z > 2.85) = =.0022 P(z > 1.66) = =.9515 P( 1.66 < z < 2.85) = = ) Use the table of standard normal probabilities to find the value z of a standard normal variable that satisfies each of the following statements. For each sketch a standard normal curve and mark your value of z on the axis. a. 25% of observations fall below it b. 40% of observations fall above it z =.67 z =.25 c. proportion less than it is 0.8 d. 90% of observations are greater than it z =.84 z = ) What are the quartiles (all three) of a standard normal distribution? Q 1 : z =.67 Q 2 : z = 0 Q 3 : z =.67 12) The deciles of any distribution are the points that mark off the lowest 10% and the highest 10%. What are the deciles of the standard normal distribution? z = 1.28 and z = 1.28

5 13) Which of the following are true statements? a. The area under a normal curve is always equal to 1, no matter what the mean and standard deviation are. b. The smaller the standard deviation of a normal curve, the higher and narrower the graph. c. Normal curves with different means are centered around different numbers. i. I and II ii. I and III iii. II and III iv. I, II, and III v. None of the above gives the complete set of true responses. 14) Which of the following are true statements? a. The area under the standard normal curve between 0 and 2 is twice the area between 0 and 1. b. The area under the standard normal curve between 0 and 2 is half the area between 2 and 2. c. For the standard normal curve, the interquartile range is approximately 3. i. I and II ii. I and III iii. II only iv. I, II and III v. None of the above gives the complete set of true responses. 15) Populations P1 and P2 are normally distributed and have identical means. However, the standard deviation of P1 is twice the standard deviation of P2. What can be said about the percentage of observations falling within two standard deviations of the mean for each population? i. The percentage for P1 is twice the percentage for P2. ii. The percentage for P1 is greater, but not twice as great, as the percentage for P2. iii. The percentage for P2 is twice the percentage for P1. iv. The percentage for P2 is greater, but not twice as great, as the percentage for P1. v. The percentages are identical.

6 16) Suppose that a college admissions office needs to compare scores of students who take the SAT with those who take the ACT. Suppose that among the college s applicants who take the SAT, scores have a mean of 896 and a standard deviation of 174. Further suppose that among the college s applicants who take the ACT, scores have a mean of 20.6 and a standard deviation of 5.2. a) If applicant Bobby scored 1080 on the SAT, how many points above the SAT mean did he score? ; 184 points above the SAT mean. b) If applicant Kathy scored 28 on the ACT, how many points above the ACT mean did she score? ; 7.4 points above the ACT mean. c) Is it sensible to conclude that since your answer to (a) is greater than your answer to b), Bobby outperformed Kathy on the admissions test? Explain. No, they are different tests with different scoring scales. d) Determine how many standard deviations above the mean Bobby scored by dividing your answer to (a) by the standard deviation of the SAT scores. Do the same for Kathy s score. Bobby: z = ; z = 1.06 Kathy: z = ; z = e) Which applicant has the higher z-score for his or her admissions test score? Kathy had the higher z-score, 1.42 > 1.06 f) Explain in your own words which applicant performed better on his or her admissions test. Kathy did better. Since she is more standard deviations above the mean she would be in a higher percentile than Bobby. g) Calculate the z-score for applicant Peter, who scored 740 on the SAT, and for applicant Kelly, who scored 19 on the ACT. Peter: z = ; z =.90 Kelly: z = ; z = h) Which of Peter and Kelly has the higher z-score? Kelly has the higher z-score, -.31 > -.90: i) Under what conditions does a z-score turn out to be negative? A z-score will be negative when a value is below the mean.

7 17) Data from the National Vital Statistics Report reveal that the distribution of the duration of human pregnancies (i.e., the number of days between conception and birth) is approximately normal with mean = 270 and standard deviation = 15. Use this normal model to determine the probability that a given pregnancy comes to term in: a. less than 244 days (which is about 8 months) b. more than 275 days (which is about 9 months) c. over 300 days d. between 260 and 280 days e. Data from the National Vital Statistics Report reveal that of 3,880,894 births in the US in 1997, the number of pregnancies that resulted in a preterm delivery, defined as 36 or fewer weeks since conception, was 436,600. Compare this to the prediction that would be obtained from the model vs ; pretty close 18) Suppose that the IQ scores of students at a certain college follow a normal distribution with mean 115 and standard deviation 12. a. Use the normal model to determine the proportion of students with an IQ score below b. Find the proportion of these undergraduates having IQs greater than c. Find the proportion of these undergraduates having IQs between 110 and d. With his IQ of 75, what would the percentile of Forrest Gump s IQ be?.04 th percentile f. Determine how high one s IQ must be in order to be in the top 1% of all IQs at this college

8 19) Suppose that Professors Wells and Zeddes have final exam scores that are approximately normally distributed with mean 75. The standard deviation of Wells scores is 10, and that of Zeddes scores is 5. a. With which professor is a score of 90 more impressive? Support your answer with appropriate probability calculations and with a sketch. Zeddes; z-score is 3 which is farther above the mean than Wells where the z-score is.33 b. With which professor is a score of 60 more discouraging? Again support your answer with appropriate probability calculations and with a sketch. Zeddes; z-score is -3 which is farther below the mean than Wells where the z-score is ) Suppose that the wrapper of a certain candy bar lists its weight as 2.13 ounces. Naturally, the weights of individual bars vary somewhat. Suppose that the weights of these candy bars vary according to a normal distribution with mean = 2.2 ounces and standard deviation = 0.04 ounces. a. What proportion of candy bars weigh less than the advertised weight?.0401 b. What proportion of candy bars weigh more than 2.25 ounces?.1056 c. What proportion of candy bars weigh between 2.2 and 2.3 ounces?.4938 d. If the manufacturer wants to adjust the production process so that only 1 candy bar in 1000 weighs less than the advertised weight, what should the mean of the actual weights be (assuming that the standard deviation of the weights remains 0.04 ounces)? μ =

9 21) A trucking firm determines that its fleet of trucks averages a mean of 12.4 miles per gallon with a standard deviation of 1.2 miles per gallon on cross-country hauls. What is the probability that one of the trucks averages fewer than 10 miles per gallon? With a z-score of -2, the probability that the trucks will average fewer than 10 mpg is ) A factory dumps an average of 2.43 tons of pollutants into a river every week. If the standard deviation is 0.88 tons, what is the probability that in a week more than 3 tons are dumped? With a z-score of 0.65, the probability that in a week more than 3 tons of pollutants are dumped is ) An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hour, what is the probability that an item will take between 3 and 4 hours? With z-scores of -0.8 and 1.2, the probability that an item will take between 3 and 4 hours to move through an assembly line is ) The mean score on a college placement exam is 500 with a standard deviation of 100. Ninety-five percent of the test takers score above what? 95% of the test takers score above ) The average noise level in a restaurant is 30 decibels with a standard deviation of 4 decibels. Ninety-nine percent of the time it is below what value? 99% of the time the average noise level in a restaurant is less than decibels. 26) The mean income per household in a certain state is $9500 with a standard deviation of $1750. The middle 95% of incomes are between what two values? With a z-score of -2, the probability that the trucks will average fewer than 10 mpg is ) Jay Olshansky from the University of Chicago was quoted in Chance News as arguing that for the average life expectancy to reach 100, 18% of people would have to live to 120. What standard deviation is he assuming for this statement to make sense (assuming life expectancies are normally distributed)? Jay Olshansky is assuming a standard deviation of approximately 21.7.

10 28) Cucumbers grown on a certain farm have weights with a standard deviation of 2 ounces. What is the mean weight if 85% of the cucumbers weigh less than 16 ounces? The mean weight is ounces if 85% of cucumbers weigh less than 16 ounces. 29) A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. If the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only 0.5% of the time? For an 8 oz cup to overflow 0.5% of the time, the mean setting should be 6.97 oz. 30) If 75% of all families spend more than $75 weekly for food, while 15% spend more than $150, what is the mean weekly expenditure and what is the standard deviation? The mean weekly food expenditure is $93.54 with a standard deviation of $ ) Three landmarks of baseball achievement are Ty Cobb s batting average of.420 in 1911, Ted Williams s.406 in 1941, and George Brett s.390 in These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the decades. The distributions are quite symmetric and reasonably normal. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts Decade Mean Std. Dev. 1910s 1940s 1970s Comparatively, who ranked highest amongst his peers? Justify your answer. Ted Williams batting average of.406 is 1941 would be ranked highest amongst his peers. Ted was 4.26 standard deviations above the mean compared to 4.15 for Ty Cobb and 4.06 for George Brett.

11 32) The following graph and data output are from the 108 years of rainfall in Austin. Let the calculated mean and standard deviation from the data represent µ and σ for the calculations. Annual Rainfall in Austin Rainfall in in S1 = mean Rainfall S2 = stddev Rainfall a) What proportion of rainfall was between 30 and 40 inches? Since the z-score for 30 inches is and the z-score for 40 inches is 0.66, the approximate proportion of rainfall between 30 and 40 inches is b) Comment on the accuracy of your calculations. The calculations should be fairly accurate. The histogram of the distribution of rainfall for Austin appears to be approximately Normal with no obvious outliers. Therefore, it is appropriate to use standard Normal probabilities. 33) A person with too much time on his hands collected 1000 pennies that came into his possession in 1999 and calculated the age (as of 1999) of each. The distribution has mean years and standard deviation years. Knowing these summary statistics but without seeing the distribution, can you comment on whether the normal distribution is likely to provide a reasonable model for these penny ages? Explain. It is probably not normally distributed (9.613) is well below 0 (a new penny). This distribution is most likely skewed to the right as there are more newer pennies in circulation. 34) Use the following data set Draw a stemplot, boxplot and normal probability plot to assess normality. Data appears to be fairly normally distributed

12 35) Use the following data set: Is this data set best modeled by using a normal distribution? Create and draw a histogram, boxplot and normal probability plot to decide. Explain your results. The histogram and box-plot both show that the data is skewed to the left. The normal probability plot has too much curvature to be considered normal.

Chapter 2. The Normal Distribution

Chapter 2. The Normal Distribution Chapter 2 The Normal Distribution Lesson 2-1 Density Curve Review Graph the data Calculate a numerical summary of the data Describe the shape, center, spread and outliers of the data Histogram with Curve

More information

Unit 16 Normal Distributions

Unit 16 Normal Distributions Unit 16 Normal Distributions Objectives: To obtain relative frequencies (probabilities) and percentiles with a population having a normal distribution While there are many different types of distributions

More information

AP Statistics Solutions to Packet 2

AP Statistics Solutions to Packet 2 AP Statistics Solutions to Packet 2 The Normal Distributions Density Curves and the Normal Distribution Standard Normal Calculations HW #9 1, 2, 4, 6-8 2.1 DENSITY CURVES (a) Sketch a density curve that

More information

STAT 155 Introductory Statistics. Lecture 5: Density Curves and Normal Distributions (I)

STAT 155 Introductory Statistics. Lecture 5: Density Curves and Normal Distributions (I) The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STAT 155 Introductory Statistics Lecture 5: Density Curves and Normal Distributions (I) 9/12/06 Lecture 5 1 A problem about Standard Deviation A variable

More information

Section 1.3 Exercises (Solutions)

Section 1.3 Exercises (Solutions) Section 1.3 Exercises (s) 1.109, 1.110, 1.111, 1.114*, 1.115, 1.119*, 1.122, 1.125, 1.127*, 1.128*, 1.131*, 1.133*, 1.135*, 1.137*, 1.139*, 1.145*, 1.146-148. 1.109 Sketch some normal curves. (a) Sketch

More information

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe

Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Introduction to the Practice of Statistics Fifth Edition Moore, McCabe Section 1.3 Homework Answers 1.80 If you ask a computer to generate "random numbers between 0 and 1, you uniform will get observations

More information

CHAPTER 6: Z-SCORES. ounces of water in a bottle. A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?

CHAPTER 6: Z-SCORES. ounces of water in a bottle. A normal distribution has a mean of 61 and a standard deviation of 15. What is the median? CHAPTER 6: Z-SCORES Exercise 1. A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words. X =. ounces of water in a bottle Exercise

More information

Numerical Measures of Central Tendency

Numerical Measures of Central Tendency Numerical Measures of Central Tendency Often, it is useful to have special numbers which summarize characteristics of a data set These numbers are called descriptive statistics or summary statistics. A

More information

Unit 21 Student s t Distribution in Hypotheses Testing

Unit 21 Student s t Distribution in Hypotheses Testing Unit 21 Student s t Distribution in Hypotheses Testing Objectives: To understand the difference between the standard normal distribution and the Student's t distributions To understand the difference between

More information

Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

More information

M 225 Test 1 A Name (1 point) SHOW YOUR WORK FOR FULL CREDIT!

M 225 Test 1 A Name (1 point) SHOW YOUR WORK FOR FULL CREDIT! M 225 Test 1 A Name (1 point) SHOW YOUR WORK FOR FULL CREDIT! Problem Max. Points Your Points 1-14 14 15 3 16 5 17 4 18 4 19 11 20 9 21 8 22 16 Total 75 1 Multiple choice questions (1 point each) 1. Look

More information

Chapter 3 Normal Distribution

Chapter 3 Normal Distribution Chapter 3 Normal Distribution Density curve A density curve is an idealized histogram, a mathematical model; the curve tells you what values the quantity can take and how likely they are. Example Height

More information

13.2 Measures of Central Tendency

13.2 Measures of Central Tendency 13.2 Measures of Central Tendency Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers

More information

Chapter 2: Exploring Data with Graphs and Numerical Summaries. Graphical Measures- Graphs are used to describe the shape of a data set.

Chapter 2: Exploring Data with Graphs and Numerical Summaries. Graphical Measures- Graphs are used to describe the shape of a data set. Page 1 of 16 Chapter 2: Exploring Data with Graphs and Numerical Summaries Graphical Measures- Graphs are used to describe the shape of a data set. Section 1: Types of Variables In general, variable can

More information

First Midterm Exam (MATH1070 Spring 2012)

First Midterm Exam (MATH1070 Spring 2012) First Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notecard. Calculators are allowed, but other electronics are prohibited. 1. [40pts] Multiple Choice Problems

More information

Histograms and density curves

Histograms and density curves Histograms and density curves What s in our toolkit so far? Plot the data: histogram (or stemplot) Look for the overall pattern and identify deviations and outliers Numerical summary to briefly describe

More information

Chapter 5: The normal approximation for data

Chapter 5: The normal approximation for data Chapter 5: The normal approximation for data Context................................................................... 2 Normal curve 3 Normal curve.............................................................

More information

AP Statistics Semester Exam Review Chapters 1-3

AP Statistics Semester Exam Review Chapters 1-3 AP Statistics Semester Exam Review Chapters 1-3 1. Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you

More information

Format: 20 True or False (1 pts each), 30 Multiple Choice (2 pts each), 4 Open Ended (5 pts each).

Format: 20 True or False (1 pts each), 30 Multiple Choice (2 pts each), 4 Open Ended (5 pts each). AP Statistics Review for Midterm Format: 20 True or False (1 pts each), 30 Multiple Choice (2 pts each), 4 Open Ended (5 pts each). These are some main topics you should know: True or False & Multiple

More information

Probability Models for Continuous Random Variables

Probability Models for Continuous Random Variables Density Probability Models for Continuous Random Variables At right you see a histogram of female length of life. (Births and deaths are recorded to the nearest minute. The data are essentially continuous.)

More information

Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2 (b) 1

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) (a) 2 (b) 1 Unit 2 Review Name Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class. 1) Miles (per day) 1-2 9 3-4 22 5-6

More information

Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs

Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)

More information

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700 Practice for Chapter 6 & 7 Math 227 This is merely an aid to help you study. The actual exam is not multiple choice nor is it limited to these types of questions. Using the following uniform density curve,

More information

2. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles.

2. Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles. Math 1530-017 Exam 1 February 19, 2009 Name Student Number E There are five possible responses to each of the following multiple choice questions. There is only on BEST answer. Be sure to read all possible

More information

AP Statistics Chapter 1 Test - Multiple Choice

AP Statistics Chapter 1 Test - Multiple Choice AP Statistics Chapter 1 Test - Multiple Choice Name: 1. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude

More information

a) Find the five point summary for the home runs of the National League teams. b) What is the mean number of home runs by the American League teams?

a) Find the five point summary for the home runs of the National League teams. b) What is the mean number of home runs by the American League teams? 1. Phone surveys are sometimes used to rate TV shows. Such a survey records several variables listed below. Which ones of them are categorical and which are quantitative? - the number of people watching

More information

University of California, Los Angeles Department of Statistics. Normal distribution

University of California, Los Angeles Department of Statistics. Normal distribution University of California, Los Angeles Department of Statistics Statistics 100A Instructor: Nicolas Christou Normal distribution The normal distribution is the most important distribution. It describes

More information

CHAPTER 7: THE CENTRAL LIMIT THEOREM

CHAPTER 7: THE CENTRAL LIMIT THEOREM CHAPTER 7: THE CENTRAL LIMIT THEOREM Exercise 1. Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews

More information

32 Measures of Central Tendency and Dispersion

32 Measures of Central Tendency and Dispersion 32 Measures of Central Tendency and Dispersion In this section we discuss two important aspects of data which are its center and its spread. The mean, median, and the mode are measures of central tendency

More information

AP * Statistics Review. Descriptive Statistics

AP * Statistics Review. Descriptive Statistics AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

More information

Probability. Distribution. Outline

Probability. Distribution. Outline 7 The Normal Probability Distribution Outline 7.1 Properties of the Normal Distribution 7.2 The Standard Normal Distribution 7.3 Applications of the Normal Distribution 7.4 Assessing Normality 7.5 The

More information

Unit 8: Normal Calculations

Unit 8: Normal Calculations Unit 8: Normal Calculations Summary of Video In this video, we continue the discussion of normal curves that was begun in Unit 7. Recall that a normal curve is bell-shaped and completely characterized

More information

Answers Investigation 4

Answers Investigation 4 Applications 1. a. Median height is 15.7 cm. Order the 1 heights from shortest to tallest. Since 1 is even, average the two middle numbers, 15.6 cm and 15.8 cm. b. Median stride distance is 124.8 cm. Order

More information

Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010

Data Mining Part 2. Data Understanding and Preparation 2.1 Data Understanding Spring 2010 Data Mining Part 2. and Preparation 2.1 Spring 2010 Instructor: Dr. Masoud Yaghini Introduction Outline Introduction Measuring the Central Tendency Measuring the Dispersion of Data Graphic Displays References

More information

Density Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties:

Density Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area under the curve must equal 1. 2. Every point on the curve

More information

3.1. Sketches will vary. Use them to confirm that students understand the meaning of (a) symmetric and (b) skewed to the left.

3.1. Sketches will vary. Use them to confirm that students understand the meaning of (a) symmetric and (b) skewed to the left. Chapter Solutions.1. Sketches will vary. Use them to confirm that students understand the meaning of (a) symmetric and (b) skewed to the left..2. (a) It is on or above the horizontal axis everywhere, and

More information

Chapter 4 The Standard Deviation as a Ruler and the Normal Model

Chapter 4 The Standard Deviation as a Ruler and the Normal Model Chapter 4 The Standard Deviation as a Ruler and the Normal Model The standard deviation is the most common measure of variation; it plays a crucial role in how we look at data. Z- scores measure standard

More information

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes

A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes A frequency distribution is a table used to describe a data set. A frequency table lists intervals or ranges of data values called data classes together with the number of data values from the set that

More information

Visual Display of Data in Stata

Visual Display of Data in Stata Lab 2 Visual Display of Data in Stata In this lab we will try to understand data not only through numerical summaries, but also through graphical summaries. The data set consists of a number of variables

More information

The Normal Distribution

The Normal Distribution Chapter 6 The Normal Distribution 6.1 The Normal Distribution 1 6.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Recognize the normal probability distribution

More information

Chapter 3. The Normal Distribution

Chapter 3. The Normal Distribution Chapter 3. The Normal Distribution Topics covered in this chapter: Z-scores Normal Probabilities Normal Percentiles Z-scores Example 3.6: The standard normal table The Problem: What proportion of observations

More information

Topic 9 ~ Measures of Spread

Topic 9 ~ Measures of Spread AP Statistics Topic 9 ~ Measures of Spread Activity 9 : Baseball Lineups The table to the right contains data on the ages of the two teams involved in game of the 200 National League Division Series. Is

More information

Remember this? We know the percentages that fall within the various portions of the normal distribution of z scores

Remember this? We know the percentages that fall within the various portions of the normal distribution of z scores More on z scores, percentiles, and the central limit theorem z scores and percentiles For every raw score there is a corresponding z score As long as you know the mean and SD of your population/sample

More information

Chapter 3: Data Description Numerical Methods

Chapter 3: Data Description Numerical Methods Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

More information

GCSE HIGHER Statistics Key Facts

GCSE HIGHER Statistics Key Facts GCSE HIGHER Statistics Key Facts Collecting Data When writing questions for questionnaires, always ensure that: 1. the question is worded so that it will allow the recipient to give you the information

More information

The Normal Curve. The Normal Curve and The Sampling Distribution

The Normal Curve. The Normal Curve and The Sampling Distribution Discrete vs Continuous Data The Normal Curve and The Sampling Distribution We have seen examples of probability distributions for discrete variables X, such as the binomial distribution. We could use it

More information

Chapter 6: Continuous Probability Distributions

Chapter 6: Continuous Probability Distributions Chapter 6: Continuous Probability Distributions Chapter 5 dealt with probability distributions arising from discrete random variables. Mostly that chapter focused on the binomial experiment. There are

More information

Exercise 1.12 (Pg. 22-23)

Exercise 1.12 (Pg. 22-23) Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

More information

Methods for Describing Data Sets

Methods for Describing Data Sets 1 Methods for Describing Data Sets.1 Describing Data Graphically In this section, we will work on organizing data into a special table called a frequency table. First, we will classify the data into categories.

More information

Histogram. Graphs, and measures of central tendency and spread. Alternative: density (or relative frequency ) plot /13/2004

Histogram. Graphs, and measures of central tendency and spread. Alternative: density (or relative frequency ) plot /13/2004 Graphs, and measures of central tendency and spread 9.07 9/13/004 Histogram If discrete or categorical, bars don t touch. If continuous, can touch, should if there are lots of bins. Sum of bin heights

More information

Unit 7: Normal Curves

Unit 7: Normal Curves Unit 7: Normal Curves Summary of Video Histograms of completely unrelated data often exhibit similar shapes. To focus on the overall shape of a distribution and to avoid being distracted by the irregularities

More information

STT 315 Practice Problems I for Sections

STT 315 Practice Problems I for Sections STT 35 Practice Problems I for Sections. - 3.7. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. ) Parking at a university has become

More information

Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

More information

Chapter 7 What to do when you have the data

Chapter 7 What to do when you have the data Chapter 7 What to do when you have the data We saw in the previous chapters how to collect data. We will spend the rest of this course looking at how to analyse the data that we have collected. Stem and

More information

STP 226 Example EXAM #1 (from chapters 1-3, 5 and 6)

STP 226 Example EXAM #1 (from chapters 1-3, 5 and 6) STP 226 Example EXAM #1 (from chapters 1-3, 5 and 6) Instructor: ELA JACKIEWICZ Student's name (PRINT): Class time: Honor Statement: I have neither given nor received information regarding this exam, and

More information

College of the Canyons Math 140 Exam 1 Amy Morrow. Name:

College of the Canyons Math 140 Exam 1 Amy Morrow. Name: Name: Answer the following questions NEATLY. Show all necessary work directly on the exam. Scratch paper will be discarded unread. One point each part unless otherwise marked. 1. Owners of an exercise

More information

III. GRAPHICAL METHODS

III. GRAPHICAL METHODS Pie Charts and Bar Charts: III. GRAPHICAL METHODS Pie charts and bar charts are used for depicting frequencies or relative frequencies. We compare examples of each using the same data. Sources: AT&T (1961)

More information

Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1

Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1 AP Statistics: 10.2: Comparing Two Means Name: Suppose we want to compare the average effectiveness of two treatments in a completely randomized experiment. In this case, the parameters µ 1 and µ 2 are

More information

AP Statistics Final Examination Multiple-Choice Questions Answers in Bold

AP Statistics Final Examination Multiple-Choice Questions Answers in Bold AP Statistics Final Examination Multiple-Choice Questions Answers in Bold Name Date Period Answer Sheet: Multiple-Choice Questions 1. A B C D E 14. A B C D E 2. A B C D E 15. A B C D E 3. A B C D E 16.

More information

Descriptive Statistics. Frequency Distributions and Their Graphs 2.1. Frequency Distributions. Chapter 2

Descriptive Statistics. Frequency Distributions and Their Graphs 2.1. Frequency Distributions. Chapter 2 Chapter Descriptive Statistics.1 Frequency Distributions and Their Graphs Frequency Distributions A frequency distribution is a table that shows classes or intervals of data with a count of the number

More information

Classify the data as either discrete or continuous. 2) An athlete runs 100 meters in 10.5 seconds. 2) A) Discrete B) Continuous

Classify the data as either discrete or continuous. 2) An athlete runs 100 meters in 10.5 seconds. 2) A) Discrete B) Continuous Chapter 2 Overview Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Classify as categorical or qualitative data. 1) A survey of autos parked in

More information

6.1 Graphs of Normal Probability Distributions. Normal Curve aka Probability Density Function

6.1 Graphs of Normal Probability Distributions. Normal Curve aka Probability Density Function Normal Distributions (Page 1 of 23) 6.1 Graphs of Normal Probability Distributions Normal Curve aka Probability Density Function Normal Probability Distribution TP TP µ! " µ µ +! x x-axis Important Properties

More information

PROPERTIES OF MEAN, MEDIAN

PROPERTIES OF MEAN, MEDIAN PROPERTIES OF MEAN, MEDIAN In the last class quantitative and numerical variables bar charts, histograms(in recitation) Mean, Median Suppose the data set is {30, 40, 60, 80, 90, 120} X = 70, median = 70

More information

MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 103/GRACEY PRACTICE EXAM/CHAPTERS 2-3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. MATH 3/GRACEY PRACTICE EXAM/CHAPTERS 2-3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) The frequency distribution

More information

JOHN W. TUKEY. Tukey was converted to statistics by the real problems experience and the real data experience during the Second World War.

JOHN W. TUKEY. Tukey was converted to statistics by the real problems experience and the real data experience during the Second World War. 74 Chapter Number and Title JOHN W. TUKEY AT&T Archives The Philosopher of Data Analysis He started as a chemist, became a mathematician, and was converted to statistics by what he called the real problems

More information

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

More information

vs. relative cumulative frequency

vs. relative cumulative frequency Variable - what we are measuring Quantitative - numerical where mathematical operations make sense. These have UNITS Categorical - puts individuals into categories Numbers don't always mean Quantitative...

More information

Empirical Rule Confidence Intervals Finding a good sample size. Outline. 1 Empirical Rule. 2 Confidence Intervals. 3 Finding a good sample size

Empirical Rule Confidence Intervals Finding a good sample size. Outline. 1 Empirical Rule. 2 Confidence Intervals. 3 Finding a good sample size Outline 1 Empirical Rule 2 Confidence Intervals 3 Finding a good sample size Outline 1 Empirical Rule 2 Confidence Intervals 3 Finding a good sample size -3-2 -1 0 1 2 3 Question How much of the probability

More information

MEASURES OF VARIATION

MEASURES OF VARIATION NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are

More information

Lab 6: Sampling Distributions and the CLT

Lab 6: Sampling Distributions and the CLT Lab 6: Sampling Distributions and the CLT Objective: The objective of this lab is to give you a hands- on discussion and understanding of sampling distributions and the Central Limit Theorem (CLT), a theorem

More information

Ch. 3.1 # 3, 4, 7, 30, 31, 32

Ch. 3.1 # 3, 4, 7, 30, 31, 32 Math Elementary Statistics: A Brief Version, 5/e Bluman Ch. 3. # 3, 4,, 30, 3, 3 Find (a) the mean, (b) the median, (c) the mode, and (d) the midrange. 3) High Temperatures The reported high temperatures

More information

2. Describing Data. We consider 1. Graphical methods 2. Numerical methods 1 / 56

2. Describing Data. We consider 1. Graphical methods 2. Numerical methods 1 / 56 2. Describing Data We consider 1. Graphical methods 2. Numerical methods 1 / 56 General Use of Graphical and Numerical Methods Graphical methods can be used to visually and qualitatively present data and

More information

Descriptive Statistics Solutions COR1-GB.1305 Statistics and Data Analysis

Descriptive Statistics Solutions COR1-GB.1305 Statistics and Data Analysis Descriptive Statistics Solutions COR-GB.0 Statistics and Data Analysis Types of Data. The class survey asked each respondent to report the following information: gender; birth date; GMAT score; undergraduate

More information

Statistics Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Statistics Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Statistics Final Exam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Assume that X has a normal distribution, and find the indicated

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Ch. 2 Methods for Describing Sets of Data 2.1 Describing Qualitative Data 1 Identify Classes/Compute Class Frequencies/Relative Frequencies/Percentages 1) In an eye color study, 25 out of 50 people in

More information

Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics

Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),

More information

( ) ( ) Central Tendency. Central Tendency

( ) ( ) Central Tendency. Central Tendency 1 Central Tendency CENTRAL TENDENCY: A statistical measure that identifies a single score that is most typical or representative of the entire group Usually, a value that reflects the middle of the distribution

More information

Mind on Statistics. Chapter 8

Mind on Statistics. Chapter 8 Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

More information

Introduction to Environmental Statistics. The Big Picture. Populations and Samples. Sample Data. Examples of sample data

Introduction to Environmental Statistics. The Big Picture. Populations and Samples. Sample Data. Examples of sample data A Few Sources for Data Examples Used Introduction to Environmental Statistics Professor Jessica Utts University of California, Irvine jutts@uci.edu 1. Statistical Methods in Water Resources by D.R. Helsel

More information

Each exam covers lectures from since the previous exam and up to the exam date.

Each exam covers lectures from since the previous exam and up to the exam date. Sociology 301 Exam Review Liying Luo 03.22 Exam Review: Logistics Exams must be taken at the scheduled date and time unless 1. You provide verifiable documents of unforeseen illness or family emergency,

More information

Frequency distributions, central tendency & variability. Displaying data

Frequency distributions, central tendency & variability. Displaying data Frequency distributions, central tendency & variability Displaying data Software SPSS Excel/Numbers/Google sheets Social Science Statistics website (socscistatistics.com) Creating and SPSS file Open the

More information

Continuous Random Variables

Continuous Random Variables Chapter 5 Continuous Random Variables 5.1 Continuous Random Variables 1 5.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Recognize and understand continuous

More information

Introduction to Descriptive Statistics

Introduction to Descriptive Statistics Mathematics Learning Centre Introduction to Descriptive Statistics Jackie Nicholas c 1999 University of Sydney Acknowledgements Parts of this booklet were previously published in a booklet of the same

More information

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1:

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1: Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1: THE NORMAL CURVE AND "Z" SCORES: The Normal Curve: The "Normal" curve is a mathematical abstraction which conveniently

More information

PROBLEM SET 1. For the first three answer true or false and explain your answer. A picture is often helpful.

PROBLEM SET 1. For the first three answer true or false and explain your answer. A picture is often helpful. PROBLEM SET 1 For the first three answer true or false and explain your answer. A picture is often helpful. 1. Suppose the significance level of a hypothesis test is α=0.05. If the p-value of the test

More information

Chapter 5 Review The Normal Probability and Standardization

Chapter 5 Review The Normal Probability and Standardization Chapter 5 Review The Normal Probability and Standardization MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) Approximately

More information

Math Chapter 3 review

Math Chapter 3 review Math 116 - Chapter 3 review Name Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations. 1) Bill kept track

More information

We will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students:

We will use the following data sets to illustrate measures of center. DATA SET 1 The following are test scores from a class of 20 students: MODE The mode of the sample is the value of the variable having the greatest frequency. Example: Obtain the mode for Data Set 1 77 For a grouped frequency distribution, the modal class is the class having

More information

F. Farrokhyar, MPhil, PhD, PDoc

F. Farrokhyar, MPhil, PhD, PDoc Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How

More information

LAMC Math 137 Test 1 Module 1-2 Yun 10/1/2014

LAMC Math 137 Test 1 Module 1-2 Yun 10/1/2014 LAMC Math 137 Test 1 Module 1-2 Yun 10/1/2014 Last name First name You may use a calculator but not a cellphone, tablet or an ipod. Please clearly mark your choices on multiple choice questions and box

More information

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice! Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!) Part A - Multiple Choice Indicate the best choice

More information

Chapter 1: Looking at Data Distributions. Dr. Nahid Sultana

Chapter 1: Looking at Data Distributions. Dr. Nahid Sultana Chapter 1: Looking at Data Distributions Dr. Nahid Sultana Chapter 1: Looking at Data Distributions 1.1 Displaying Distributions with Graphs 1.2 Describing Distributions with Numbers 1.3 Density Curves

More information

Comment on the Tree Diagrams Section

Comment on the Tree Diagrams Section Comment on the Tree Diagrams Section The reversal of conditional probabilities when using tree diagrams (calculating P (B A) from P (A B) and P (A B c )) is an example of Bayes formula, named after the

More information

8.8 APPLICATIONS OF THE NORMAL CURVE

8.8 APPLICATIONS OF THE NORMAL CURVE 8.8 APPLICATIONS OF THE NORMAL CURVE If a set of real data, such as test scores or weights of persons or things, can be assumed to be generated by a normal probability model, the table of standard normal-curve

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name 1) A recent report stated ʺBased on a sample of 90 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company -hired truck drivers.ʺ Does

More information

Previous lecture. Lecture 6. Learning outcomes of this lecture. Today. Entering data into SPSS. Data coding. Data preparation methods

Previous lecture. Lecture 6. Learning outcomes of this lecture. Today. Entering data into SPSS. Data coding. Data preparation methods Lecture 6 Empirical Research Methods IN4304 Data preparation methods Previous lecture participant-observation and non-participant observation Does the observer act as a member of the group? Sampling strategies

More information

Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods

Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods Desciptive Statistics Qualitative data Quantitative data Graphical methods Numerical methods Qualitative data Data are classified in categories Non numerical (although may be numerically codified) Elements

More information

1 Measures for location and dispersion of a sample

1 Measures for location and dispersion of a sample Statistical Geophysics WS 2008/09 7..2008 Christian Heumann und Helmut Küchenhoff Measures for location and dispersion of a sample Measures for location and dispersion of a sample In the following: Variable

More information

2. A is a subset of the population. 3. Construct a frequency distribution for the data of the grades of 25 students taking Math 11 last

2. A is a subset of the population. 3. Construct a frequency distribution for the data of the grades of 25 students taking Math 11 last Math 111 Chapter 12 Practice Test 1. If I wanted to survey 50 Cabrini College students about where they prefer to eat on campus, which would be the most appropriate way to conduct my survey? a. Find 50

More information