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6-9

6-9. Data Distributions . Objective Create and interpret box-and-whisker plots. . Reading Math. The first quartile is sometimes called the lower quartile, and the third quartile is sometimes called the upper quartile.

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6-9

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  1. 6-9 Data Distributions • Objective • Create and interpret box-and-whisker plots.

  2. Reading Math The first quartile is sometimes called the lower quartile, and the third quartile is sometimes called the upper quartile. Another way to describe a data set is how the data values are spread out from the center. Quartiles divide a data set into four equal parts. Each quartile contains one-fourth of the values in the set. First quartile:median of the lower half of the data set Second quartile: median of the whole data set Third quartile: median of the upper half of the data set

  3. Interquartile range (IQR)is the difference between the third and first quartiles. It represents the range of the middle half of the data.

  4. First quartile Third quartile Minimum   A box-and-whisker plot can be used to show how the values in a data set are distributed. You need five values to make a box and whisker plot minimum (or lowest value) first quartile Median third quartile maximum (or greatest value). Maximum Median   

  5. Minimum Maximum Q2 Q3 Q1 6 10 12 20 3 Example 1: Application The number of runs scored by a softball team in 19 games is given. Use the data to make a box-and-whisker plot. 3, 8, 10, 12, 4, 9, 13, 20, 12, 15, 10, 5, 11, 5, 10, 6, 7, 6, 11 Step 1 Order the data from least to greatest. 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 13, 15, 20 Step 2 Identify the five needed values. 3, 4, 5, 5, 6, 6, 7, 8, 9, 10, 10, 10, 11, 11,12, 12, 13, 15, 20

  6. First quartile Third quartile Minimum Maximum Median      0 8 16 24 Example 1Continued Step 3 Draw a number line and plot a point above each of the five needed values. Draw a box through the first and third quartiles and a vertical line through the median. Draw lines from the box to the minimum and maximum.

  7. Minimum Maximum Q2 Q3 Q1 13 14 18 23 11 You Try!Example 2 Use the data to make a box-and-whisker plot. 13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23 Step 1 Order the data from least to greatest. 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 17, 18, 18, 19, 22, 23 Step 2 Identify the five needed values. 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 17, 18, 18, 19,22, 23

  8. First quartile Third quartile Maximum Minimum Median • • • • • 8 16 24 You Try!Example 2 Continued Step 3 Draw a number line and plot a point above each of the five needed values.

  9. Example 3: Reading and Interpreting Box-and-Whisker Plots The box-and-whisker plots show the number of mugs sold per student in two different grades. A. About how much greater was the median number of mugs sold by the 8th grade than the median number of mugs sold by the 7th grade? about 5 B. Which data set has a greater maximum? Explain. 8th grade; point for maximum is farther to the right for the 8th grade than for the 7th grade

  10. 50% of all the numbers are between Q1 and Q3 This is called the Inter-Quartile Range (IQR) median max min Q2 Q1 3 7 9 12 14 15 17 18 40 IQR = 8 17 - 9 = 8

  11. To determine if a number is an outlier, multiply the IQR by 1.5 8 • 1.5 = 12 median max min Q2 Q1 3 7 9 12 14 15 17 18 40 IQR = 8 An outlier is any number that is 12 less than Q1 or 12 more than Q3

  12. Example 4 Given a 5 number summary, provide two outliers. One outlier should be greater than Q3 and one outlier should be less than Q1. 3, 6, 10, 12, 20 Q1 Q3 Step 1 Identify Q1 and Q3. =6 12 – 6 Step 2Calculate the IQR. =9 6(1.5) Step 3 Calculate the outlier factor. Any number that is 9less than Q1 or 9more than Q3 Examples: -3 or 21

  13. Classwork/Homework 6-9Worksheet

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