Students will learn to display and analyze data in box-and-whisker plots.

Vocabulary box-and-whisker plot lower quartile upper quartile interquartile range

A box-and-whisker plot divides the data into five parts: While central tendency describes the middle of a data set, variability describes how spread out the data are. A box-and-whisker plot uses a number line to show how data are distributed and to illustrate the variability of a data set. A box-and-whisker plot divides the data into five parts: Measures of Variation Min and Max: the lowest and highest of the data set. First Quartile or lower quartile is the median of the lower half of the data. Second Quartile is the median of the data set. Third Quartile or upper quartile is the median of the upper half of the data.

More Measures of Variation Interquartile Range is the range in the middle of the data. It is the difference between the upper and lower quartiles in a data set. Range is the difference between the greatest and least values in a data set.

EXAMPLE 1 Make a box-and-whisker plot SONG LENGTHS The lengths of songs (in seconds) on a CD are listed below. Make a box-and-whisker plot of the song lengths. 173, 206, 179, 257, 198, 251, 239, 246, 295, 181, 261 SOLUTION Order: the data. Then find the median and the quartiles. STEP 1

EXAMPLE 1 Make a box-and-whisker plot STEP 2 Plot the median, the quartiles, the maximum value, and the minimum value below a number line. STEP 3 Draw a box from the lower quartile to the upper quartile. Draw a vertical line through the median. Draw a line segment (a “whisker”) from the box to the maximum and another from the box to the minimum.

GUIDED PRACTICE You Try…. 1. Make a box-and-whisker plot of the ages of eight family members: 60, 15, 25, 20, 55, 70, 40, 30. 15 22.5 35 57.5 70 Step 1: Order: the data. Step 2: Plot the 5-Variation Step 3: Draw a box

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots Additional Example 1: You Do…. Use the data to make a box-and-whisker plot. 73 67 75 81 67 75 85 69 Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles. The least value. The greatest value. 67 69 73 75 81 85 67 69 73 75 81 85 + Find the median. 2 =74 Step 1: Order: the data. Step 2: Plot the 5-Variation Step 3: Draw a box

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots Additional Example 1 Continued Step 1 Continued 67 69 73 75 81 85 67 + 69 lower quartile = = 68 2 75 + 81 upper quartile = = 78 2

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots Additional Example 1 Continued Step 2: Draw a number line. Above the number line, plot points for each value in Step 1. Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median. Then draw the “whiskers” from the box to the least and greatest values. 64 66 68 70 72 74 76 78 80 82 84 86

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots You Do… Use the data to make a box-and-whisker plot. 42 22 31 27 24 38 35 Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles. The least value. The greatest value. 22 24 27 31 35 38 42 22 24 27 31 35 38 42 The median. The upper and lower quartiles. 22 24 27 31 35 38 42

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots You Do…: Example 1 Continued Step 2: Draw a number line. Above the number line, plot a point for each value in Step 1. Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median. Then draw the “whiskers” from the box to the least and greatest values. 20 22 24 26 28 30 32 34 36 38 40 42

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots You Do…#2 : Comparing Box-and-Whisker Plot Use the box-and-whisker plots below to answer each question. Basketball Players Baseball Players 64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.) Which set of heights of players has a greater median? The median height of basketball players, about 74 inches, is greater than the median height of baseball players, about 70 inches.

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots You Do #2…: Comparing Box-and-Whisker Plot Use the box-and-whisker plots below to answer each question. Basketball Players Baseball Players 64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.) Which players have a greater interquartile range? The basketball players have a longer box, so they have a greater interquartile range.

Reflection CAN YOU make a box-and-whisker plot? Explain each steps?

Box-and-Whisker Plots Course 2 7-5 Box-and-Whisker Plots Lesson Quiz: On your Desk… Use the data for Questions 1-3. 24, 20, 18, 25, 22, 32, 30, 29, 35, 30, 28, 24, 38 1. Create a box-and-whisker plot for the data. 2. What is the range? 3. What is the 3rd quartile? 20 31 18 20 22 24 26 28 30 32 34 36 38 40