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Example 6-3b Objective Construct and interpret box-and-whisker plots

Example 6-3b Vocabulary Lower quartile The median of the lower half of the data set

Example 6-3b Vocabulary Upper quartile The median of the upper half of the data set

Example 6-3b Vocabulary Box-and-whisker plot A diagram that summarizes data by dividing it into 4 parts

Example 6-3b Vocabulary Lower extreme The least value of the data set

Example 6-3b Vocabulary Upper extreme The greatest value of the data set

Example 6-3b Vocabulary Interquartile range The difference between the upper quartile and the lower quartile

Lesson 6 Contents Example 1Construct a Box-and-Whisker Plot Example 2Analyze Data Example 3Identify and Plot Outliers

Example 6-1a NUTRITION The grams of fat per serving of items from the meat, poultry, and fish food group are shown in the table. Make a box-and-whisker plot of the data. 7Tuna18Ground beef 9Trout10Fried shrimp 9Sardines 3Fish sticks 5Salmon 3Crabmeat 5Roast beef16Bologna 19Pork chop15Beefsteak 14Ham 9Bacon Fat (gm)ItemFat (gm)Item Nutrition Facts Order data from least to greatest 3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19 1/3

3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19 Example 6-1a Find median median: 9 Count the pieces of data and divide by 2 14 divided by 2 = 7 Beginning at smallest number, underline 7 pieces of data Beginning at largest number, underline 7 pieces of data Circle the 2 middle numbers Find the mean of the numbers 1/3

3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19 Example 6-1a lower quartile: median of lower half = 5 Find median of the first half of the data Count the pieces of data and divide by 2 7 divided by 2 = 3.5 Beginning at smallest number, underline 3 pieces of data Beginning at largest number, underline 3 pieces of data Circle the middle number that was not underlined 1/3

3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19 Example 6-1a lower quartile: median of lower half = 5 Find median of the second half of the data Count the pieces of data and divide by 2 7 divided by 2 = 3.5 Beginning at smallest number, underline 3 pieces of data Beginning at largest number, underline 3 pieces of data Circle the middle number that was not underlined upper quartile: median of upper half = 15 1/3

3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19 Example 6-1a lower quartile: median of lower half = 5 upper quartile: median of upper half = 15 Smallest Number = Lower Quartile = Median = Upper Quartile = Largest Number = Identify the following /3

Example 6-1a Smallest Number = Lower Quartile = Median = Upper Quartile = Largest Number = Identify the following Draw a number line and plot the data above the number line 1/3

Example 6-1a Draw a rectangle using the LQ and UQ for the ends Draw a vertical line through the median Draw a horizontal line from the lowest number to the LQ Draw a horizontal line from the highest number to the UQ Answer: 1/3

Example 6-1b ATTENDANCE The number of students attending class each day are shown in the table. Make a box-and-whisker plot of the data. Attendance Answer: 1/3

Example 6-2a HOCKEY The table shows the ten all-time leading scorers in the National Hockey League through a recent season. Make a box-and-whisker plot of the data. Then use it to describe how the data are spread. NHL Leading Scorers PlayerGoalsPlayerGoals Wayne Gretzky894Steve Yzerman645 Gordie Howe801Phil Esposito717 Marcel Dionne731Ray Bourque410 Mark Messler627Mario Lemieux648 Ron Francis487Paul Coffey396 Order data from least to greatest 396, 410, 487, 627, 645, 648, 717, 731, 801, 894 2/3

Example 6-2a 396, 410, 487, 627, 645, 648, 717, 731, 801, 894 Find median Count the pieces of data and divide by 2 10 divided by 2 = 5 Beginning at smallest number, underline 5 pieces of data Beginning at largest number, underline 5 pieces of data Circle the 2 middle numbers Find the mean of the numbers median: /3

Example 6-2a 396, 410, 487, 627, 645, 648, 717, 731, 801, 894 median: /3 Find median of the first half of the data Count the pieces of data and divide by 2 5 divided by 2 = 2.5 Beginning at smallest number, underline 2 pieces of data Beginning at largest number, underline 2 pieces of data lower quartile: median of lower half = 487 Circle the middle number

Example 6-2a 396, 410, 487, 627, 645, 648, 717, 731, 801, 894 median: /3 Find median of the second half of the data Count the pieces of data and divide by 2 5 divided by 2 = 2.5 Beginning at smallest number, underline 2 pieces of data Beginning at largest number, underline 2 pieces of data lower quartile: median of lower half = 487 Circle the middle number Upper quartile: median of upper half = 731

Example 6-1a Smallest Number = Lower Quartile = Median = Upper Quartile = Largest Number = Identify the following /3 396, 410, 487, 627, 645, 648, 717, 731, 801, 894 lower quartile: median of lower half = 487 Upper quartile: median of upper half = 731 median: 646.5

Example 6-1a Smallest Number = Lower Quartile = Median = Upper Quartile = Largest Number = Identify the following /3 Draw a number line and plot the data above the number line

Example 6-1a 1/3 Draw a rectangle using the LQ and UQ for the ends Draw a vertical line through the median Draw a horizontal line from the lowest number to the LQ Draw a horizontal line from the highest number to the UQ

Example 6-1a 1/3 Describe how the data are spread. The graph shows that ½ the players scored between 487 and 731 Answer:

Example 6-2b COMMUTE The table below shows the commute time from home to school for fifteen middle school students. Make a box-and-whisker plot of the data. Then use it to describe how the data are spread. Commute Time /3

Example 6-2b Answer: The graph shows that half of the students travel between 10 and 21 minutes. The largest range of the four quartiles is from 21 to 46. 2/3

Example 6-3a CANDY SALES Twelve members of the music club sold candy bars as a fund-raiser. The table shows the number of candy bars sold by each person. Make a box-and- whisker plot of the data. 23, 27, 39, 46, 46, 51, 53, 54, 55, 60, 69, Candy Sold per Student 3/3 Order data from least to greatest

Example 6-3a 23, 27, 39, 46, 46, 51, 53, 54, 55, 60, 69, 81 3/3 Find median Count the pieces of data and divide by 2 12 divided by 2 = 6 Beginning at smallest number, underline 6 pieces of data Beginning at largest number, underline 6 pieces of data Circle the 2 middle numbers Find the mean of the numbers median: 52

Example 6-3a 23, 27, 39, 46, 46, 51, 53, 54, 55, 60, 69, 81 3/3 Count the pieces of data and divide by 2 6 divided by 2 = 3 Beginning at smallest number, underline 3 pieces of data Beginning at largest number, underline 3 pieces of data Circle the 2 middle numbers Find the mean of the numbers median: 52 Find median of the first half of the data lower quartile: median of lower half = 42.5

Example 6-3a 23, 27, 39, 46, 46, 51, 53, 54, 55, 60, 69, 81 3/3 Count the pieces of data and divide by 2 6 divided by 2 = 3 Beginning at smallest number, underline 3 pieces of data Beginning at largest number, underline 3 pieces of data Circle the 2 middle numbers Find the mean of the numbers median: 52 Find median of the second half of the data lower quartile: median of lower half = 42.5 Upper quartile: median of upper half = 57.5

Example 6-3a 3/3 Identify the following Smallest Number = Lower Quartile = Median = Upper Quartile = Largest Number = Outlier = , 27, 39, 46, 46, 51, 53, 54, 55, 60, 69, 81 Notice there is an outlier in this data set Plot the outlier but do not use it as the largest number in the box-and-whisker plot 81 69

Example 6-3a 3/3 Identify the following Smallest Number = Lower Quartile = Median = Upper Quartile = Largest Number = Outlier = Draw a number line and plot the data above the number line

Example 6-3a 3/3 Draw a rectangle using the LQ and UQ for the ends Draw a vertical line through the median Draw a horizontal line from the lowest number to the LQ Draw a horizontal line from the highest number to the UQ Answer:

Example 6-3b BASKETBALL The table below shows the number of points scored by the leading scorer of a basketball team during the past twelve games. Make a box-and- whisker plot of the data Points Scored Answer: 3/3

End of Lesson 6 Assignment Lesson 2:6Box-and-Whisker Plots All