Unit 8 Guided Notes. Statistics Standards: S.IC.1, S.IC.3, S.IC.4, S.IC.5, S.IC.6, S.ID.4 Clio High School Algebra 2B

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1 Unit 8 Guided Notes Statistics Standards: S.IC.1, S.IC.3, S.IC.4, S.IC.5, S.IC.6, S.ID.4 Clio High School Algebra 2B Name: Period: Miss Seitz s tutoring: Tuesdays and Thursdays after school Website with all videos and resources Miss Kari Seitz Text: Classroom: kseitz@clioschools.org Concept # What we will be learning... Text Measures of Central Tendency Calculate measures of central tendency 11.6 Draw and interpret box-and-whisker plots Calculating Standard Deviation Find standard deviation and variance 11.7 Applying Standard Deviation Apply standard deviation and variance 11.7 Samples and Surveys Explain that statistics involves drawing conclusions about a population based on the results obtained from a random sample of the population Describe the differences among sample surveys, experiments and observational studies Apply random sampling techniques to draw a sample from a population Use data from a sample to make statements about the whole population Explain the purpose of using a sample survey, experiment or observational study Choose and defend a method for research in a particular situation Check for bias Normal Distribution Use the mean and standard deviation to sketch a normal bell curve Use the way data is distributed to estimate the size of a population Look at data sets and decide if they are normally distributed

2 Measures of Central Tendency Text: 11.6 Calculate measures of central tendency Draw and interpret box-and-whisker plots Vocabulary: mean, median, mode, box-and-whisker plot Definitions A M of C T indicates the middle of the data set. M is It is written sum of the data values number of data values and read x bar M is the middle number of the data set. To find it, arrange all terms in order and find the middle term. If there is an even number of terms, find the mean of the two middle values. M is the most frequently occurring value(s) in a data set. Finding Measures of Central Tendency Example 1: The frequency table shows the number of trees in the yard of each house on one street. What are the mean, median and mode for the trees per yard? Mean Sum of the data values Number of data values Median List each value from smallest to largest the number of times it occurs. Then, find the middle number. Mode The most frequently occurring value(s) You Try It! 1.) Find the mean, median and mode of 98, 87, 78, 82, 101, 99, 97, 97, 102, 91, 93

3 An O is a value that is substantially different from the other values in the data set. They can affect the measures of central tendency. Q are numbers that divide an ordered data set into four parts. Each part contains the same number of data values. A B - - W P is a way to display data that uses Quartiles to bound the center box The minimum and maximum values to form the whiskers Identifying Outliers Example 2: Identify the outlier for the data set Definitions Creating a Box-and-Whisker Plot Example 2: Create a Box-and-Whisker Plot for 2, 8, 3, 7, 3, 6, 4, 9, 10, 15, 21, 29, 32, 30 Steps: 1. Put the values in order and find the median 2. Find the First Quartile (the median of the lower half) Find the Third Quartile (the median of the upper half) 4. Plot your minimum, maximum and quartile values above a number line 5. Create the box and whiskers You Try It! 2.) Create a box-and-whisker plot for 77, 79, 80, 86, 87, 87, 94, 99, 100

4 Calculating Standard Deviation Text: 11.7 Find standard deviation and variance Vocabulary: standard deviation, variance The S D shows how much data values deviate from the mean. Definitions The V is the value you get when you square the Standard Deviation. It is represented by the Greek letter sigma σ It is represented as σ 2 Calculating Standard Deviation Example 1: Calculate the mean, standard deviation and variance of 52, 63, 65, 77, 80, 82 Steps: 1. Find the mean 2. Complete the table x x - (x - ) 2 Add the last column 3. Divide the sum of the last column by the number of values in your data set to find the variance (σ 2 ) 4. Take the square root of the variance to find the standard deviation (σ)

5 You Try It! 1.) Find the standard deviation. 6, 13, 12, 9, 10

6 Applying Standard Deviation Text: 11.7 Apply standard deviation and variance Vocabulary: N/A Describing Data Using Standard Deviation We can describe data using the standard deviation. Each value in a data list falls within some number of standard deviations of the mean. Example 1: The mean is 50 and the standard deviation is 10. Example 2: Within how many standard deviations from the mean do the values fall? Mean: 35 Standard Deviation: 5 Values: 12, 18, 29, 42, 54 If a value, x, is between 40 and 60, x falls within one standard deviation of the mean. Application Problems Example 3: The table displays the number of U.S. hurricane strikes by decade from the years 1851 to Within how many standard deviations from the mean do all of the values fall? Steps: 1. Find the mean and standard deviation 2. Plot the mean and all values on a number line to see within how many standard deviations each value lies.

7 You Try It! 1.) The table shows the number of hurricanes in the Atlantic Ocean from 1992 to Within how many standard deviations of the mean do all of the values fall?

8 Samples and Surveys Text: 11.8 Explain that statistics involves drawing conclusions about a population based on the results obtained from a random sample of the population Describe the differences among sample surveys, experiments and observational studies Apply random sampling techniques to draw a sample from a population Use data from a sample to make statements about the whole population Explain the purpose of using a sample survey, experiment or observational study Choose and defend a method for research in a particular situation Check for bias Vocabulary: population, sample, sample type, sample method, bias Definitions A P is all of the members of a set Example: Students at Clio High School Example: Citizens of the United States A S is a part of the population Example: Brown haired people in a classroom Example: Left-handed people in the school B is a systematic error introduced by the sampling method. This happens when part of the population is overrepresented or underrepresented. Sampling Types and Methods Convenience Sample: Choose any members of the population who are conveniently and readily available Random Sample: All members of the population are equally likely to be chosen Self-Selected Sample: Choose any members of the population who volunteer for the sample Systematic Sample: Order the population in some way, then select from it at regular intervals Analyzing Sample Methods Example 1: A newspaper wants to find out what percent of the city population favors a property tax increase to raise money for local parks. What is the sampling method used for each situation? Does the sample have a bias? Explain your reasoning. A. A newspaper article on the tax increase invites readers to express their opinions on the newspaper s website. B. A reporter interviews people leaving the city s largest park. C. A survey calls every 50 th listing from the local phone book.

9 Study Methods In an observational study, you measure or observe members of a sample in such a way that they are not affected by the study. In a controlled experiment you divide the sample into two groups. You impose a treatment on one group but not on the other control group. Then, you compare the effect on the treated group to the control group. In a survey, you ask every member of the sample set of questions. Analyzing Study Methods Example 2: Which type of study method is described in each situation? Should the sample statistics be used to make a general conclusion about the population? A. Researchers randomly choose two groups from 10 volunteers. Over a period of 8 weeks, one group eats ice cream before going to sleep, and the other does not. Volunteers wear monitoring devices while sleeping, and researchers record dream activity. B. Students in a science class record the height of bean plants as they grow. C. Student council members ask every tenth student in the lunch line if they like the cafeteria food. You Try It! 1.) Suppose a study for pharmaceutical company includes 500 participants of a variety of ages, 350 of which are female. After accounting for overall health, they find that the drug has a significant effect over 50% of the time. Should the sample statistics be used to make a general conclusion about the effectiveness of the drug in the larger population? Explain your reasoning.

10 Normal Distribution Text: Use the mean and standard deviation to sketch a normal bell curve Use the way data is distributed to estimate the size of a population Look at data sets and decide if they are normally distributed Vocabulary: normal distribution, normal curve, positively skewed, negatively skewed, bell curve Definitions A N D has data that varies randomly from the mean. In a Normal Distribution: % of all data values fall within one standard deviation of the mean % of all data values fall within two standard deviations of the mean % of all data values fall within three standard deviations of the mean The graph of a Normal Distribution is called a Normal Curve. It looks like a bell that centers on the mean. Skewed Data Data values that are not normally distributed are skewed. The graph does not look like a symmetric curve. Normally Distributed P S N S Analyzing Normally Distributed Data Example 1: The bar graph gives the weights of a population of female brown bears. The red curve shows how the weights are normally distributed about the mean (115 kg). Approximately what percent of female brown bears weigh less than 120 kg?

11 Sketching a Normal Curve Example 2: Sketch a normal curve for the distribution. Label the x-axis values at 1, 2, and 3 standard deviations from the mean. Mean = 45 Standard Deviation = 2 Analyzing a Normal Distribution Example 3: The scores on the Algebra 2 final are approximately normally distributed with a mean of 150 and a standard deviation of 15. What percentage of the students who took the test scored above 180? Steps: 1. Sketch a rough normal curve to describe your data 2. Identify where 180 falls on the normal curve 3. Add the percentages from 180 and up You Try It! 1.) Sketch a normal curve for the distribution. Label the x-axis values at 1, 2, and 3 standard deviations from the mean. Mean = 45 Standard Deviation = ) Use the information from Example 3. If 250 students took the final exam, approximately how many scored above 135?