# SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Do Now: Explain how this graph could be misleading.

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SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Do Now: Explain how this graph could be misleading.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Do Now: The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginning price. The histogram below shows the distribution of total returns for all 1528 stocks listed on the New York State Exchange in one year. This is a histogram of the percents in each class rather than a histogram of counts. (a) Describe the overall shape of the distribution of total returns. (b) What is the approximate center of this distribution? (c) Approximately what were the smallest and largest total returns? (Describe the spread of the distribution)

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary The Interquartile Range (IQR) To calculate the quartiles: Arrange the observations in increasing order and locate the median M. The first quartile Q1 is the median of the observations located to the left of the median in the ordered list. The third quartile Q3 is the median of the observations located to the right of the median in the ordered list. The interquartile range (IQR) is defined as: IQR = Q3 – Q1 (this measures the range of the middle 50%)

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Example: Find and Interpret the IQR for the travel times to work for 20 randomly selected New Yorkers.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Use the IQR rule to identify outliers: 1.5 x IQR

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary The five-number summary: The five-number summary of a distribution consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest. In symbols, the five-number summary is Minimum Q1 M Q3 Maximum This five number summary leads to a new graph displayed as Boxplot: A graph of the five-number summary.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Example 1: The 2009 roster of the Dallas Cowboys professional football team included 10 offensive linemen. Their weights (in pounds) were 338 318 353 313 318 326 307 317 311 311 a) Find the five-number summary for these data by hand. Show your work. b) Calculate the IQR. Interpret this value in context. c) Determine whether there are any outliers using the 1.5 × IQR rule. d) Draw a boxplot of the data.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Example 2: Barry Bonds set the major league record by hitting 73 home runs in a single season in 2001. On August 7, 2007, Bonds hit his 756th career home run, which broke Hank Aaron’s longstanding record of 755. By the end of the 2007 season when Bonds retired, he had increased the total to 762. Here are data on the number of home runs that Bonds hit in each of his 21 complete seasons: 16, 25, 24, 19, 33, 25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 26, 28 a) Find the five-number summary for these data by hand. Show your work. b) Calculate the IQR. Interpret this value in context. c) Determine whether there are any outliers using the 1.5 × IQR rule. d) Draw a boxplot of the data.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Do Now: a)Determine the five number summary for the data. b)Find the IQR. c)Are there any outliers? d)Create a boxplot of your data.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Example: Let’s examine data on the number of pets owned by a group of 9 children. Here are the data, arranged from lowest to highest: 1 3 4 4 4 5 7 8 9 Variance: The average squared distance of the observations in a data set from their mean. Standard Deviation: s x measures the average distance of the observations from their mean.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Example 1: The heights (in inches)of the five starters on a basketball team are 67, 72, 76, 76, and 84. (a) Find and interpret the mean. (b) Make a table that shows, for each value, its deviation from the mean and its squared deviation from the mean. (c) Show how to calculate the variance and standard deviation from the values in your table. Interpret the meaning of the standard deviation in this setting.

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary Example 2: The first four students to arrive for a first-period statistics class were asked how much sleep (to the nearest hour) they got last night. Their responses were 7, 7, 9, and 9. (a) Find the standard deviation from its definition. (b) Interpret the value of s x you obtained in (a). (c) Do you think it’s safe to conclude that the mean amount of sleep for all 30 students in this class is close to 8 hours? Why or why not?

SWBAT: Measure standard deviation, identify outliers, and construct a boxplot using the five-number summary *The median and IQR are usually better than the mean and standard deviation for describing a skewed distribution or a distribution with strong outliers. *Use x and s x only for reasonably symmetric distributions that don’t have outliers.

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