6-3 Measures of Variation I CAN make a box-and-whisker plot. I CAN find the interquartile range of a set of numbers. I CAN find the mean absolute deviation of a set of numbers.

6-3 Measures of Variation Vocabulary box-and-whisker plot quartiles variation interquartile range (IQR) mean absolute deviation

6-3 Measures of Variation Ms. Snow asks some of her students how many pets they have. The responses are 9, 0, 4, 1, 1, 2, 3, 5, and 2 pets. You can display this data using a box-and-whisker plot. A box-and-whisker plot or box plot is a data display that shows how data are distributed by using the median, quartiles, least value, and greatest value. Quartiles are three values, one of which is the median, that divide a data set into fourths. Each quartile contains one-fourth, or 25%, of the data.

6-3 Measures of Variation Example 1: Making a Box-and-Whisker Plot The average number of hours that several students watch television in a day is given. Use the data to make a box-and-whisker plot: 2, 1, 5, 2, 1, 2, 3, 2, 2. Step 1 Order the data from least to greatest. 1, 1, 2, 2, 2, 2, 2, 3, 5 Step 2 Find the least and greatest values, the median, and the first and third quartiles Least value Greatest Value Third Quartile Median First Quartile

6-3 Measures of Variation Step 3 Draw a number line, and plot a point above each of the five values you just identified. Draw a box through the first and third quartiles and a vertical line through the median. Draw lines from the box to the least value and the greatest value. (These are the whiskers.) Continued: Example

6-3 Measures of Variation You Try! Example 1 The next 9 customers in line are waiting to purchase the following number of items: 6, 10, 8, 5, 9, 4, 10, 7, 5. Use the data to make a box- and-whisker plot. Step 1 Order the data from least to greatest. 4, 5, 5, 6, 7, 8, 9, 10, 10 Step 2 Find the least and greatest values, the median, and the first and third quartiles Least value First Quartile Median Third Quartile Greatest Value

6-3 Measures of Variation Continued: You Try! Example 1 Step 3 Draw a number line, and plot a point above each of the five values you just identified. Draw a box through the first and third quartiles and a vertical line through the median. Draw lines from the box to the least value and the greatest value. (These are the whiskers.)

6-3 Measures of Variation CAN YOU make a box-and-whisker plot?

6-3 Measures of Variation Lesson Quiz A park ranger measures the thickness of ice on a lake in 8 different locations: 19 in., 17 in., 15 in., 15 in., 18 in., 12 in., 16 in., 14 in. Make a box-and-whisker plot of the data.

6-3 Measures of Variation HOMEWORK

6-3 Measures of Variation A box-and-whisker plot can be used to show how the values in a data set are distributed. Variation (variability) is the spread of the values. The interquartile range (IQR) is the difference between the first and third quartiles. It is a measure of the spread of the middle 50% of the data. A small interquartile range means that the data in the middle of the set are close in value. A large interquartile range means that the data in the middle are spread out.

6-3 Measures of Variation Example 2: Finding the Interquartile Range Find the interquartile range for the data set 17, 39, 38, 9, 29, 40, 27 9, 17, 27, 29, 38, 39, 40 38,29,9,17,27,4039, Find the median and quartiles IQR=39-17=22Find the difference between the first quartile (17) and the third quartile (39). The interquartile range is 22. Order the data from least to greatest.

6-3 Measures of Variation You Try! Example 2 Find the interquartile range for the data set 87, 71, 72, 73, 84, 92, , 72, 73, 73, 84, 87, 92 84,73,71,72,73,9287, Find the median and quartiles IQR=87-72=15Find the difference between the first quartile (72) and the third quartile (87). The interquartile range is 15. Order the data from least to greatest.

6-3 Measures of Variation Another measure of variation is the mean absolute deviation. Mean absolute deviation is the mean amount that data values differ from the mean of the data values.

6-3 Measures of Variation = is 0.5 unit from is 6.5 units from is 2.5 units from is 8.5 units from Example 3: Finding Mean Absolute Deviation A scientist is studying temperature variation. She determines that the temperature at noon on four days is 75F, 82F, 78F, and 67F. What is the mean absolute deviation of the temperatures? Find the mean.. Find the distance on a number line each data value is from the mean. each data value is from the mean. Find the mean

6-3 Measures of Variation Continued: Example = Find the mean of the distances The mean absolute deviation of the temperatures is 4.5F. So, on average, the temperatures were within 4.5F of the mean, 75.5F.

6-3 Measures of Variation You Try! Example 3 A scientist is studying temperature variation. She determines that the temperature at noon on four days is 64F, 75F, 80F, and 78F. What is the mean absolute deviation of the temperatures? Find the mean = is units from is 0.75 unit from is 5.75 units from is 3.75 units from Find the mean Find the distance on a number line each data value is from the mean.

6-3 Measures of Variation Continued: You Try! Example 3 Find the mean of the distances = The mean absolute deviation of the temperatures is 5.125F. So, on average, the temperatures were within is 5.125F of the mean, 74.25F.

6-3 Measures of Variation CAN YOU find the interquartile range for a set of numbers? CAN YOU find the mean absolute deviation for a set of numbers?

6-3 Measures of Variation Lesson Quiz A park ranger measures the thickness of ice on a lake in 8 different locations: 19 in., 17 in., 15 in., 15 in., 18 in., 12 in., 16 in., 14 in. 1. Find the interquartile range of the data. 3 in. 2. Find the mean absolute deviation of the data in.

6-3 Measures of Variation HOMEWORK