9 3 Histograms and Box Plots Students will

9 -3 Histograms and Box Plots Students will learn to display and analyze data in box-and-whisker plots.

9 -3 Histograms and Box Plots Vocabulary box-and-whisker plot lower quartile upper quartile interquartile range

9 -3 Histograms and Box Plots While central tendency describes the middle of a data set, variability describes how spread out the data are. A box-andwhisker plot uses a number line to show data are distributed and to illustrate the variability of a data set. A box-and-whisker plot divides the data into five parts: Min and Max: the lowest Measures of Variation 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.

9 -3 Histograms and Box Plots More Measures of Variation Range is the difference between the greatest and least values in a data set. 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.

9 -3 EXAMPLE 1 Histograms and Box plot Plots Make a box-and-whisker 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 STEP 1 Order: the data. Then find the median and the quartiles.

9 -3 EXAMPLE 1 Histograms and Box plot Plots Make a box-and-whisker STEP 2 STEP 3 Plot the median, the quartiles, the maximum value, and the minimum value below a number line. 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.

9 -3 and Box Plots GUIDED Histograms PRACTICE You Try…. Make a box-and-whisker plot of the ages of eight family members: 60, 15, 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

9 -3 7 -5 Box-and-Whisker Histograms and Box. 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. 67 67 69 73 75 75 81 85 67 67 69 73+75 75 81 85 2 =74 Step 1: Order: the data. Course 2 The least value. The greatest value. Find the median. Step 2: Plot the 5 -Variation Step 3: Draw a box

9 -3 7 -5 Box-and-Whisker Histograms and Box. Plots Additional Example 1 Continued Step 1 Continued 67 67 69 73 75 75 81 85 lower quartile = upper quartile = Course 2 67 + 69 = 68 2 75 + 81 = 78 2

9 -3 7 -5 Box-and-Whisker Histograms and Box. 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 Course 2 66 68 70 72 74 76 78 80 82 84 86

9 -3 7 -5 Box-and-Whisker Histograms and Box. 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. 22 24 27 31 35 38 42 The greatest value. Course 2 22 24 27 31 35 38 42 The median. 22 24 27 31 35 38 42 The upper and lower quartiles.

9 -3 7 -5 Box-and-Whisker Histograms and Box. 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 Course 2 22 24 26 28 30 32 34 36 38 40 42

9 -3 7 -5 Box-and-Whisker Histograms and Box. 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 t 66 68 70 72 74 76 78 80 82 84 Heights of Basketball and Baseball Players (in. ) 86 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. Course 2

9 -3 7 -5 Box-and-Whisker Histograms and Box. 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 t 66 68 70 72 74 76 78 80 82 84 Heights of Basketball and Baseball Players (in. ) 86 Which players have a greater interquartile range? The basketball players have a longer box, so they have a greater interquartile range. Course 2

9 -3 Histograms and Box Plots Reflection CAN YOU make a box-and-whisker plot? Explain each steps?

9 -3 7 -5 Box-and-Whisker Histograms and Box. Plots Lesson Quiz: On your Desk… Use the data for Questions 1 -3. 24, 20, 18, 25, 22, 30, 29, 35, 30, 28, 24, 38 1. Create a box-and-whisker plot for the data. 2. What is the range? 20 3. What is the 3 rd quartile? 31 18 Course 2 20 22 24 26 28 30 32 34 36 38 40