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

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 Reading Math The first quartile is sometimes called the lower quartile, and the third quartile is sometimes called the upper quartile.

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

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 1.minimum (or lowest value) 2.first quartile 3.Median 4.third quartile 5.maximum (or greatest value). Median First quartileThird quartile      MinimumMaximum

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 Q1 6 Q3 12 Q2 10 Minimum 3 Maximum 20

Example 1 Continued Median First quartileThird quartile     MinimumMaximum 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.

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 You Try! Example 2 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 Q1 13 Q3 18 Q2 14 Minimum 11 Maximum 23

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

The box-and-whisker plots show the number of mugs sold per student in two different grades. Example 3: Reading and Interpreting Box-and- Whisker Plots 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

50% of all the numbers are between Q1 and Q3 This is called the Inter-Quartile Range (IQR) = IQR = 8 minmaxmedianQ1Q2

IQR = 8 To determine if a number is an outlier, multiply the IQR by = 12 An outlier is any number that is 12 less than Q1 or 12 more than Q3 minmaxmedianQ1Q2

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. Step 1 Identify Q1 and Q3. Q1 3, 6, 10, 12, 20 Q3 Step 2 Calculate the IQR. 12 – 6=6 Step 3 Calculate the outlier factor. 6(1.5)=9 Any number that is 9 less than Q1 or 9 more than Q3 Examples: -3 or 21

Classwork/Homework 6-9 Worksheet