# Statistics Review Solutions

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Statistics Review Solutions 1. Katrina must take five exams in a math class. If her scores on the first four exams are 71, 69, 85, and 83, what score does she need on the fifth exam for her overall mean to be at least 90? In order to determine the answer to this question, we would need to add all 5 exam scores together and divide the sum by 5. This needs to equal 90. Since we don't have all 5 exam scores, we need to go back a step and just figure out what all the exams need to add up to so that when we divide that number by 5, we get 90. In other words, we need to determine what number divided by 5 is equal 90. This number is 5 times 90 which is 450. All 5 exams need to add up to 450. The exams we have so far add up to 308 ( = 300). We only have one exam left to get to 450, thus that exam score must be 142 ( = 142). Thus it is not possible for Katrina to score high enough on the fifth exam to get an average 90 (this is assuming that each test is worth 100 points). 2. Todd Booth, an avid jogger, kept detailed records the number miles he ran per week during the past year. The frequency distribution below summarized his records. Find the mean, median, and mode the number miles per week that Todd ran. Miles Run Number per Week Weeks Although I am finding the mean and median without a calculator here, you will be able to use a calculator on the exam to find the mean, median, and standard deviation.

2 MEAN: To find the mean number miles, you need to add all the numbers miles from each week together and divide by the number stores surveyed. The sum all the numbers miles is (Notice: since the number weeks next to 0 is 5, I have to add in 0 five times.) = 172 I now divide the sum by 52 since that is the number weeks recorded. This will give me a mean 172/52 = MEDIAN: The median number miles is the number miles in the middle when all the numbers are put in order. Since there are 52 numbers, the middle is in between the 26th and 27th number miles. We will take these two numbers miles, add them together and divide by two. The 26th number miles is 3. The 27th number miles is 3. Thus the median is (3 + 3)/2 = 3 MODE: The mode number miles is the number miles that occurs in the most weeks. This is easy to see from the table. The number miles that occurs in the most weeks is 2 since there are 10 weeks with that number miles and 4 since there are 10 weeks with that number miles. Thus the data is bimodal with the number miles 2 and 4 both being modes. 3. The mean salary 12 men is \$52,000, and the mean salary 4 women is \$84,000. Find the mean salary all 16 people. To find a mean, we need to add all the 16 salaries together and divide by 16. Since we don't have individual salaries, we need to settle for the totals amount made by the 12 men and the total amount made by the 4 women. We can find the total amount the salaries the 12 men by multiplying the mean salary the 12 men by 12. This will give us a total \$ We can find the total amount the salaries the 4 women by multiplying the mean salary the 4 women by 4. This will give us a total \$ If we add these two totals together, we get the sum salaries all 16 people. This sum is \$ Now all we need to do to find the mean is divide this total

3 by 16. This will give us a mean \$60000 for all 16 people. 4. The frequency distribution below lists the results a quiz given in Pressor Gilbert's statistics class. Score Number Students a. Find the mean and standard deviation the scores. b. What percent the data lies within one standard deviation the mean? c. What percent the data lies within two standard deviations the mean? d. What percent the data lies within three standard deviations the mean? e. Draw a histogram to illustrate the data. a. These we will not calculate by hand (although we could use either the formulas given in the notes to do these calculation). According to the calculator, the mean the scores is 8 and the standard deviation the quiz scores is which we will round to b. To find what percent the data falls within one standard deviation the mean, we need to find how many the students have quiz scores within one standard deviation the mean. What this mean is that we need to find a quiz score one standard deviation below the mean ( = ) and a quiz score one standard deviation above the mean ( = ). We now want to put a mark on the table to show where

4 happens (between 6 and 7) and a mark on the table to show where happens (between 9 and 10). Since I can't mark the table, I will shade in the number stores that would fall between the two marks. Score Number Students We now need to add together the shaded numbers to find how many students have quiz scores which fall within one standard deviation the mean. This number is = 24. To find the percentage scores that fall within one standard deviation the mean, we will take 24, divide it by 34 (since there are 34 total student scores) and multiply that by 100 (to change from a decimal to a percent). This will give us (24/34)*100= 70.6%.

5 c. To find what percent the data falls within two standard deviations the mean, we need to find how many the students have quiz scores within two standard deviations the mean. What this means is that we need to find a quiz score two standard deviations below the mean ( = 5.129) and a quiz score two standard deviations above the mean ( = ). We now want to put a mark on the table to show where happens (between 5 and 6) and a mark on the table to show where happens (above 10). Since I can't mark the table, I will shade in the number stores that would fall between the two marks. Score Number Students We now need to add together the shaded numbers to find how many students have quiz scores which fall within two standard deviations the mean. This number is = 32. To find the percentage scores that fall within two standard deviations the mean, we will take 32, divide it by 34 (since there are 34 total exam scores) and multiply that by 100 (to change from a decimal to a percent). This will give us (32/34)*100= 94.12%. d. To find what percent the data falls within three standard deviations the mean, we need to find how many the students have quiz scores within three standard deviations the mean. What this means is that we need to find a quiz score three standard deviations below the mean ( = ) and a quiz score two standard deviations above the mean ( = ). We now want to put a mark on the table to show where happens (below 5) and a mark on the table to show where happens (above 10).

6 Since I can't mark the table, I will shade in the number stores that would fall between the two marks. Score Number Students We now need to add together the shaded numbers to find how many students have quiz scores which fall within two standard deviations the mean. This number is = 34. To find the percentage scores that fall within two standard deviations the mean, we will take 34, divide it by 34 (since there are 34 total exam scores) and multiply that by 100 (to change from a decimal to a percent). This will give us (34/34)*100= 100%. e.

7 5. To examine the effects a new registration system, a campus newspaper asked freshmen how long they had to wait in a registration line. The frequency distribution is given below. Complete the frequency distribution and draw a histogram to illustrate the data. x = time in minutes number freshmen 0 x < x < x < x < x < x < n = The first step in the answer is to add up the numbers in the right column to find n. Here the numbers add up to 700. Thus n = 700. To draw the histogram, you place the numbers in the left column along the bottom the horizontal axis (x-axis) and write a label below that saying that it represents time in minutes. You now label the vertical axis (y-axis) with the word frequency or the title the right column. You also need to determine a scale for the vertical axis. Since by numbers go from 51 to 237, going by 50s would make sense. We could also choose to go by 20s, but that would require several more tick marks along the axis. Remember that the labels on the horizontal axis go at the beginning and ending the bar when the data is grouped (given in intervals). The histogram would look like the one below.

8 6. The frequency distribution below summaries the hourly wages the workers at ASU food service. Complete the frequency distribution and draw a histogram to illustrate the data. x = hourly wage number employees \$ 4.00 x < \$ \$ 5.50 x < \$ \$ 7.00 x < \$ \$ 8.50 x < \$ \$ x < \$ \$ x < \$ n = The first step in the answer is to add up the numbers in the right column to find n. Here the numbers add up to 152. Thus n = 152. To draw the histogram, you place the numbers in the left column along the bottom the horizontal axis (x-axis) and write a label below that saying that it represents hourly wage. You now label the vertical axis (y-axis) with the word frequency or the title the right column. You

9 also need to determine a scale for the vertical axis. Since by numbers go from 9 to 42, going by 10s would make sense. Remember that the labels on the horizontal axis go at the beginning and ending the bar when the data is grouped (given in intervals). The histogram would look like the one below.

### Statistics Revision Sheet Question 6 of Paper 2

Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of

### Homework 3. Part 1. Name: Score: / null

Name: Score: / Homework 3 Part 1 null 1 For the following sample of scores, the standard deviation is. Scores: 7, 2, 4, 6, 4, 7, 3, 7 Answer Key: 2 2 For any set of data, the sum of the deviation scores

### STATISTICS FOR PSYCH MATH REVIEW GUIDE

STATISTICS FOR PSYCH MATH REVIEW GUIDE ORDER OF OPERATIONS Although remembering the order of operations as BEDMAS may seem simple, it is definitely worth reviewing in a new context such as statistics formulae.

### MAT 142 College Mathematics Module #3

MAT 142 College Mathematics Module #3 Statistics Terri Miller Spring 2009 revised March 24, 2009 1.1. Basic Terms. 1. Population, Sample, and Data A population is the set of all objects under study, a

### 6.4 Normal Distribution

Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under

### 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

### Statistics Summary (prepared by Xuan (Tappy) He)

Statistics Summary (prepared by Xuan (Tappy) He) Statistics is the practice of collecting and analyzing data. The analysis of statistics is important for decision making in events where there are uncertainties.

### 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

### 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

### Math 1011 Homework Set 2

Math 1011 Homework Set 2 Due February 12, 2014 1. Suppose we have two lists: (i) 1, 3, 5, 7, 9, 11; and (ii) 1001, 1003, 1005, 1007, 1009, 1011. (a) Find the average and standard deviation for each of

### Calculation example mean, median, midrange, mode, variance, and standard deviation for raw and grouped data

Calculation example mean, median, midrange, mode, variance, and standard deviation for raw and grouped data Raw data: 7, 8, 6, 3, 5, 5, 1, 6, 4, 10 Sorted data: 1, 3, 4, 5, 5, 6, 6, 7, 8, 10 Number of

### Elementary Statistics. Summarizing Raw Data. In Frequency Distribution Table

Summarizing Raw Data In Frequency Distribution Table 1 / 37 What is a Raw Data? Raw Data (sometimes called source data) is data that has not been processed for meaningful use. What is a Frequency Distribution

### ( ) ( ) 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

### Chapter 3: Central Tendency

Chapter 3: Central Tendency Central Tendency In general terms, central tendency is a statistical measure that determines a single value that accurately describes the center of the distribution and represents

### EXAMPLE To paraphrase Benjamin Disraeli: "There are lies, darn lies, and DAM STATISTICS."

PART 3 MODULE 2 MEASURES OF CENTRAL TENDENCY EXAMPLE 3.2.1 To paraphrase Benjamin Disraeli: "There are lies, darn lies, and DAM STATISTICS." Compute the mean, median and mode for the following DAM STATISTICS:

### 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)

### ! x sum of the entries

3.1 Measures of Central Tendency (Page 1 of 16) 3.1 Measures of Central Tendency Mean, Median and Mode! x sum of the entries a. mean, x = = n number of entries Example 1 Find the mean of 26, 18, 12, 31,

### Lesson Plan. Vocabulary

S.ID.6c: Use Residuals to Assess Fit of a Function S.ID.6c: Use Residuals to Assess Fit of a Function Summarize, represent, and interpret data on two categorical and quantitative variables 6. Represent

### Lecture I. Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions.

Lecture 1 1 Lecture I Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions. It is a process consisting of 3 parts. Lecture

### Chapter 2: Frequency Distributions and Graphs

Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct

### CHAPTER 3 CENTRAL TENDENCY ANALYSES

CHAPTER 3 CENTRAL TENDENCY ANALYSES The next concept in the sequential statistical steps approach is calculating measures of central tendency. Measures of central tendency represent some of the most simple

### LIFTING A LOAD NAME. Materials: Spring scale or force probes

Lifting A Load 1 NAME LIFTING A LOAD Problems: Can you lift a load using only one finger? Does it always take the same amount of force to lift a load? Where should you press to lift a load with the least

### Descriptive Statistics

Chapter 2 Descriptive Statistics 2.1 Descriptive Statistics 1 2.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Display data graphically and interpret graphs:

### Graphical and Tabular. Summarization of Data OPRE 6301

Graphical and Tabular Summarization of Data OPRE 6301 Introduction and Re-cap... Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful information

### Measures of Center Section 3-2 Definitions Mean (Arithmetic Mean)

Measures of Center Section 3-1 Mean (Arithmetic Mean) AVERAGE the number obtained by adding the values and dividing the total by the number of values 1 Mean as a Balance Point 3 Mean as a Balance Point

### WHICH TYPE OF GRAPH SHOULD YOU CHOOSE?

PRESENTING GRAPHS WHICH TYPE OF GRAPH SHOULD YOU CHOOSE? CHOOSING THE RIGHT TYPE OF GRAPH You will usually choose one of four very common graph types: Line graph Bar graph Pie chart Histograms LINE GRAPHS

### Information Technology Services will be updating the mark sense test scoring hardware and software on Monday, May 18, 2015. We will continue to score

Information Technology Services will be updating the mark sense test scoring hardware and software on Monday, May 18, 2015. We will continue to score all Spring term exams utilizing the current hardware

### 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

### Graphs and charts - quiz

Level A 1. In a tally chart, what number does this represent? A) 2 B) 4 C) 8 D) 10 2. In a pictogram if represents 2 people, then how many people do these symbols represent? A) 3 people B) 5 people C)

### Using SPSS, Chapter 2: Descriptive Statistics

1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,

### 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,

### 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.

### Describing, Exploring, and Comparing Data

24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter

### Session 1.6 Measures of Central Tendency

Session 1.6 Measures of Central Tendency Measures of location (Indices of central tendency) These indices locate the center of the frequency distribution curve. The mode, median, and mean are three indices

### HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

### Probability Distributions

CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution

### 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

### 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,

### Lesson Plan. Mean Count

S.ID.: Central Tendency and Dispersion S.ID.: Central Tendency and Dispersion Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape

### Determine whether the data are qualitative or quantitative. 8) the colors of automobiles on a used car lot Answer: qualitative

Name Score: Math 227 Review Exam 1 Chapter 2& Fall 2011 ********************************************************************************************************************** SHORT ANSWER. Show work on

### 3.2 Measures of Central Tendency

3. Measures of Central Tendency outlier an element of a data set that is very different from the others mean a measure of central tendency found by dividing the sum of all the data by the number of pieces

### Descriptive Statistics

Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web

### Using SPSS 20, Handout 3: Producing graphs:

Research Skills 1: Using SPSS 20: Handout 3, Producing graphs: Page 1: Using SPSS 20, Handout 3: Producing graphs: In this handout I'm going to show you how to use SPSS to produce various types of graph.

### Associative Property The property that states that the way addends are grouped or factors are grouped does not change the sum or the product.

addend A number that is added to another in an addition problem. 2 + 3 = 5 The addends are 2 and 3. area The number of square units needed to cover a surface. area = 9 square units array An arrangement

### 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

### This activity will show you how to use Excel to draw cumulative frequency graphs. 0 < x < x < x

Pay rates for men and women Excel 2003 activity This activity will show you how to use Excel to draw cumulative frequency graphs. Information sheet The table gives the results from a survey about hourly

### Chapter 5: The normal approximation for data

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

### Fractions, decimals and percentages

Fractions, decimals and percentages Some notes for the lesson. Extra practice questions available. A. Quick quiz on units Some of the exam questions will have units in them, and you may have to convert

### Report of for Chapter 2 pretest

Report of for Chapter 2 pretest Exam: Chapter 2 pretest Category: Organizing and Graphing Data 1. "For our study of driving habits, we recorded the speed of every fifth vehicle on Drury Lane. Nearly every

### Using Excel for descriptive statistics

FACT SHEET Using Excel for descriptive statistics Introduction Biologists no longer routinely plot graphs by hand or rely on calculators to carry out difficult and tedious statistical calculations. These

### Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

### 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

### Lesson 4 Measures of Central Tendency

Outline Measures of a distribution s shape -modality and skewness -the normal distribution Measures of central tendency -mean, median, and mode Skewness and Central Tendency Lesson 4 Measures of Central

### Statistical Inference

Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this

### 10-3 Measures of Central Tendency and Variation

10-3 Measures of Central Tendency and Variation So far, we have discussed some graphical methods of data description. Now, we will investigate how statements of central tendency and variation can be used.

### Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8

Ma KEY STAGE 3 Mathematics test TIER 6 8 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

### 5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.

The Normal Distribution C H 6A P T E R The Normal Distribution Outline 6 1 6 2 Applications of the Normal Distribution 6 3 The Central Limit Theorem 6 4 The Normal Approximation to the Binomial Distribution

### Bar Graphs and Dot Plots

CONDENSED L E S S O N 1.1 Bar Graphs and Dot Plots In this lesson you will interpret and create a variety of graphs find some summary values for a data set draw conclusions about a data set based on graphs

### A.2 Measures of Central Tendency and Dispersion

Section A. Measures of Central Tendency and Dispersion A A. Measures of Central Tendency and Dispersion What you should learn How to find and interpret the mean, median, and mode of a set of data How to

### Joint Frequency Distributions. Lecture 6--Monday, Sept 27, 2010 Announcements. Lecture 6--Monday, Sept 27, 2010 Announcements 2 HOURS ONLY

Lecture 6--Monday, Sept 27, 2010 Announcements Join PRS depending on the side of the room you are sitting on! Right side (as you look at the screens) use: < x >, < y > Left side (as you look at the screens)

### 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

### Statistics Chapter 2

Statistics Chapter 2 Frequency Tables A frequency table organizes quantitative data. partitions data into classes (intervals). shows how many data values are in each class. Test Score Number of Students

### MATH 1473: Mathematics for Critical Thinking. Study Guide and Notes for Chapter 4

MATH 1473: Mathematics for Critical Thinking The University of Oklahoma, Dept. of Mathematics Study Guide and Notes for Chapter 4 Compiled by John Paul Cook For use in conjunction with the course textbook:

### Name: Date: Use the following to answer questions 2-3:

Name: Date: 1. A study is conducted on students taking a statistics class. Several variables are recorded in the survey. Identify each variable as categorical or quantitative. A) Type of car the student

### Comments 2 For Discussion Sheet 2 and Worksheet 2 Frequency Distributions and Histograms

Comments 2 For Discussion Sheet 2 and Worksheet 2 Frequency Distributions and Histograms Discussion Sheet 2 We have studied graphs (charts) used to represent categorical data. We now want to look at a

### Activity 3.7 Statistical Analysis with Excel

Activity 3.7 Statistical Analysis with Excel Introduction Engineers use various tools to make their jobs easier. Spreadsheets can greatly improve the accuracy and efficiency of repetitive and common calculations;

### Summarizing Scores with Measures of Central Tendency: The Mean, Median, and Mode

Summarizing Scores with Measures of Central Tendency: The Mean, Median, and Mode Outline of the Course III. Descriptive Statistics A. Measures of Central Tendency (Chapter 3) 1. Mean 2. Median 3. Mode

### Equations. #1-10 Solve for the variable. Inequalities. 1. Solve the inequality: 2 5 7. 2. Solve the inequality: 4 0

College Algebra Review Problems for Final Exam Equations #1-10 Solve for the variable 1. 2 1 4 = 0 6. 2 8 7 2. 2 5 3 7. = 3. 3 9 4 21 8. 3 6 9 18 4. 6 27 0 9. 1 + log 3 4 5. 10. 19 0 Inequalities 1. Solve

### Means, Medians, and Modes

8.1 Means, Medians, and Modes 8.1 OBJECTIVES 1. Calculate the mean 2. Interpret the mean 3. Find the median 4. Interpret the median 5. Find a mode A very useful concept is the average of a group of numbers.

### Measurement & Data Analysis. On the importance of math & measurement. Steps Involved in Doing Scientific Research. Measurement

Measurement & Data Analysis Overview of Measurement. Variability & Measurement Error.. Descriptive vs. Inferential Statistics. Descriptive Statistics. Distributions. Standardized Scores. Graphing Data.

### 1-2 Mean, Median, Mode, and Range

Learn to find the mean, median, mode, and range of a data set. mean median mode range outlier Vocabulary The mean is the sum of the data values divided by the number of data items. The median is the middle

### 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

### 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

### Chapter 2 - Graphical Summaries of Data

Chapter 2 - Graphical Summaries of Data Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data. Raw data is often difficult to make sense

### MCQ S OF MEASURES OF CENTRAL TENDENCY

MCQ S OF MEASURES OF CENTRAL TENDENCY MCQ No 3.1 Any measure indicating the centre of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of: (a) Skewness (b)

### 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,

### 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

### sum of the values X = = number of values in the sample n sum of the values number of values in the population

Topic 3: Measures of Central Tendency With any set of numerical data, there is always a temptation to summarise the data to a single value that attempts to be a typical value for the data There are three

### Descriptive Statistics Lesson 3 Measuring Variation 33

Descriptive Statistics Lesson 3 Measuring Variation 33 3.1- What is Data Variation? Data variation is a numeric value which measures the spread of data from the mean. For example, the two sets of numbers

### 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.

### Table 2-1. Sucrose concentration (% fresh wt.) of 100 sugar beet roots. Beet No. % Sucrose. Beet No.

Chapter 2. DATA EXPLORATION AND SUMMARIZATION 2.1 Frequency Distributions Commonly, people refer to a population as the number of individuals in a city or county, for example, all the people in California.

### 2.3. Measures of Central Tendency

2.3 Measures of Central Tendency Mean A measure of central tendency is a value that represents a typical, or central, entry of a data set. The three most commonly used measures of central tendency are

### Central Tendency & Graphs of Data Long-Term Memory Review Grade 7 Review 1

Review 1 1. The is the difference between the largest and smallest values in a set of numerical data. The is the middle value in a set of ordered data. 2. Bob took five tests in math class. His scores

### Point and Interval Estimates

Point and Interval Estimates Suppose we want to estimate a parameter, such as p or µ, based on a finite sample of data. There are two main methods: 1. Point estimate: Summarize the sample by a single number

### CC Investigation 5: Histograms and Box Plots

Content Standards 6.SP.4, 6.SP.5.c CC Investigation 5: Histograms and Box Plots At a Glance PACING 3 days Mathematical Goals DOMAIN: Statistics and Probability Display numerical data in histograms and

### Chapter 2 Describing Variables

Chapter 2 Describing Variables 2.1 Frequency Distributions for Discrete and Continuous Variables 2.2 Grouped and Cumulative Distributions 2.3 Graphing Frequency Distributions Frequency Distributions Frequency

### STT315 Chapter 4 Random Variables & Probability Distributions KM. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables

Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables Discrete vs. continuous random variables Examples of continuous distributions o Uniform o Exponential o Normal Recall: A random

### STA201 Intermediate Statistics Lecture Notes. Luc Hens

STA201 Intermediate Statistics Lecture Notes Luc Hens 15 January 2016 ii How to use these lecture notes These lecture notes start by reviewing the material from STA101 (most of it covered in Freedman et

### 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

### 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

### A Picture Really Is Worth a Thousand Words

4 A Picture Really Is Worth a Thousand Words Difficulty Scale (pretty easy, but not a cinch) What you ll learn about in this chapter Why a picture is really worth a thousand words How to create a histogram

### 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

### Common Tools for Displaying and Communicating Data for Process Improvement

Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot

### 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

### TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

### Areas of numeracy covered by the professional skills test

Areas of numeracy covered by the professional skills test December 2014 Contents Averages 4 Mean, median and mode 4 Mean 4 Median 4 Mode 5 Avoiding common errors 8 Bar charts 9 Worked examples 11 Box and

### List the elements of the given set that are natural numbers, integers, rational numbers, and irrational numbers. (Enter your answers as commaseparated

MATH 142 Review #1 (4717995) Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Description This is the review for Exam #1. Please work as many problems as possible

### MODUL 8 MATEMATIK SPM ENRICHMENT TOPIC : STATISTICS TIME : 2 HOURS

MODUL 8 MATEMATIK SPM ENRICHMENT TOPIC : STATISTICS TIME : 2 HOURS 1. The data in Diagram 1 shows the body masses, in kg, of 40 children in a kindergarten. 16 24 34 26 30 40 35 30 26 33 18 20 29 31 30