Box & WhiskerPlots

Box & Whisker PlotsObjectives:7.4.01 Collect, organize, analyze, and display data (including box plots and histograms) to solve problems.

7.4.02 Calculate, use, and interpret the mean, median, mode, range, frequency distribution, and interquartile range for a set of data.

7.4.03 Describe how the mean, median, mode, range, frequency distribution, and inter-quartile range of a set of data affect its graph.

Essential Question: What is the purpose of organizing data sets into a box and whisker plot?

What is a Box & Whisker Plot:Box & Whisker Plots

Lower Extreme

(MIN)

Lower Quartile

(Q1)Median

(Q2)Upper

Quartile(Q3)

Upper Extreme(MAX)

Vocabulary:Box & Whisker Plot: a diagram that summarizes data using the median, the upper and lower quartiles, and the extreme values.Upper Extreme: the greatest value in a set of data.Lower Extreme: the smallest value in a set of data.Upper Quartile: the median of the upper half of a set of data; UQ.Lower Quartile: the median of the lower half of a set of data; LQ.Interquartile Range: the range of the middle half of a set of data; UQ – LQ.

Box & Whisker Plots

One More Example:Box & Whisker Plots

Why Box & Whisker Plots:- Box and whisker plots use the median, upper and lower quartiles, and the extreme (least and greatest) values to summarize data. - It allows you to see important characteristics of the data at a glance.- Even though they can be difficult to create, they can provide a great amount of important information.

Box & Whisker Plots

Box & Whisker PlotsExample 1: Nutrition FactsThe 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 Beef16Bologna19Pork Chop15Beefsteak14Ham 9 Bacon

Fat (gm)ItemFat (gm) Item

Box & Whisker PlotsExample 1: Nutrition Facts

3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19

Step 2: Find the Median, L/U Quartiles, and L/U Extremes.Step 1: Order the data from least to greatest.

Median: 9

Lower Quartile is median of

lower half = 5

Upper Quartile ismedian of upper

half = 15

Lower Extreme: 3

Upper Extreme: 19

Fat Fat9 14

15 1916 53 53 9

10 918 7

Box & Whisker PlotsExample 1: Nutrition Facts

Step 4: Find the median and the quartiles.

Step 3: Draw a number line. The scale should include the median, the quartiles, and the lower and upper extremes. Graph the values as points above the.

Box & Whisker PlotsExample 1: Nutrition Facts

The graph shows that half of the foods have between 3 and 9 grams of fat. The largest range of the four quartiles is from 9 to 15. One-fourth of the foods were within this range.

Box & Whisker PlotsExample 2: NHL Leading ScorersThe 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.

Player Goals Player GoalsWayne Gretzky 894 Steve Yzerman 645Gordie Howe 801 Phil Esposito 717Marcel Dionne 731 Ray Bourque 410Mark Messier 627 Mario Lemieux 648Ron Francis 487 Paul Coffey 396

Box & Whisker PlotsExample 2: NHL Leading Scorers

396, 410, 487, 627, 645, 648, 717, 731, 801, 894

Step 2: Find the Median, Quartiles, Extremes.Step 1: Order the data from least to greatest.

Median: 646.5

Lower Quartile is Median of lower half = 487

Upper Quartile is Median of upper half = 731

Goals Goals894 645801 717731 410627 648487 396

Lower Extreme: 396

Upper Extreme: 894

Box & Whisker PlotsExample 2: NHL Leading Scorers

Step 4: Find the median and the quartiles.

Step 3: Draw a number line. The scale should include the median, the quartiles, and the lower and upper extremes. Graph the values as points above the.

Box & Whisker PlotsExample 2: NHL Leading Scorers

The graph shows that half of the players scored between 487 and 731 points. The largest range of the four quartiles is from 731 to 894. One-fourth of the players scored within this range.

Independent Practice Problems:Box & Whisker Plots

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.

Student Commute Time

25 14 7 18 1046 21 5 11 1823 17 9 13 12

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.

Independent Practice Problems:Box & Whisker Plots

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. 55395446

5381465160276923

Candy Sold Per Student

Why Calculate Outliers:Box & Whisker Plots

- First, remember that statistics assume all our data values are clustered around some central value

- For a box and whisker plot, the IQR tells how spread out the "middle" values are

- But it can also be used to tell when some of the other values are "too far" from the central value

- Any value that is "too far away" is called an "outlier," because it "lies outside" the range in which we expect it to be

Calculating OutliersBox & Whisker Plots

If we want to determine whether a data point is an outlier, we have to do the following:

Step 1: Calculate the Interquartile Range (IQR) for our stem and Leaf Plot.

IQR = Q3 – Q1

Step 2: Take the Interquartile Range (IQR) and multiply it by 1.5.

IQR x 1.5Step 3: Find:

Q1 – (IQR x 1.5) AND Q3 + (IQR x 1.5)

Box & Whisker PlotsExample 2: NHL Leading Scorers

396, 410, 487, 627, 645, 648, 710, 731, 801, 894

Looking back at this data set we can determine if any outliers exist

Median: 646.5

Lower Quartile is Median of lower half = 487

Upper Quartile is Median of upper half = 731

Goals Goals894 645801 717731 410627 648487 396

Lower Extreme: 396

Upper Extreme: 894

Box & Whisker PlotsExample 2: NHL Leading ScorersLooking back at this data set we can determine if any outliers exist.

Goals Goals894 645801 717731 410627 648487 396

LE = 396 LQ (Q1) = 487 M = 646.5 UQ (Q3) = 731 UE = 894

IQR = Q3 – Q1IQR = 731 – 487

IQR = 244

IQR x 1.5 = 244 x 1.5 = 366

487 – 366121

731 + 3661097

Box & Whisker PlotsExample 3: Box & Whisker Plots (Additional)Use a stem and leaf plot to graph the following test scores from a recent math test in Mr. Blue’s class:

76, 76, 76, 77, 80, 80, 80, 81, 81, 82, 84, 85, 88, 89, 89, 89, 89, and 92

Box & Whisker PlotsExample 4: Stem & Leaf Plots (Additional)The set of data listed below shows the number of home runs Babe Ruth hit during his career from 1914 to 1935. Make a box and whisker plot of the data. Then use it to describe how the data are spread.

Home Run Data: 0, 54, 25, 46, 4, 59, 47, 41, 3, 35, 60, 34, 2, 41, 54, 6, 11, 22, 46, 29, 46, and 49.

Box & Whisker PlotsExample 4: Stem & Leaf Plots (Additional)Home Run Data: 0, 54, 25, 46, 4, 59, 47, 41, 3, 35, 60, 34, 2, 41, 54, 6, 11, 22, 46, 29, 46, and 49.

HOMEWORK

Box & Whisker Plots

Box & Whisker PlotsExample 5: Applying Box & Whisker PlotsNow lets use the Percents Test Data to create a Box and Whisker Plot of the data and then use it to describe the spread of the data.

BOYS SCORES99, 36, 16, 23, 69, 58, 59, 21, 53, 19, 21, 82, 30, 85, 70, 81, 66, 42, 53, 52, 22, 56, 43, 57, 88, 80, 53, 86, 64, 84,

68, 79, 57, and 82

GIRLS SCORES73, 37, 61, 53, 37, 38, 24, 30, 75, 93, 65, 85, 60, 92, 80, 56, 80, 65, 77, 64, 95, 99, 82, 75, 94, 98, 63, 58, 69, 56,

95, 77, and 45

Stem & Leaf vs. Box & WhiskerLeaf (Girls Data)StemLeaf (Boys Data)

0 123456789

40 7 7 853 6 6 80 1 3 4 5 5 93 5 5 7 70 0 2 52 3 4 5 5 8 9

9 63 2 1 1

6 03 2

9 8 7 7 6 3 3 3 29 8 6 4

9 08 6 5 4 2 2 1 0

9