6.2 - Boxplots and Five Number Summaries

6.2 - Boxplots and Five Number Summaries

Unit 6 - Statistics

Math I Honors

Mr. Coleman

Learning Objectives

• Develop and interpret box and whisker plots

• Develop and interpret a "five number summary" for a data set 

• Analyze box and whisker plots for shape, center, and spread

• Compare two datasets by their box and whisker plots

Box and Whisker Plots (aka Boxplots)

• Minimum - "lowest" data point

• 1st Quartile (Q1) - median of lower 1/2 of the dataset (left of median)

• Median - as the name implies

• 3rd Quartile (Q3) - median of the upper 1/2 of dataset (right of median)

• Maximum - "Highest" data point

Multiple Choice

What was the highest score?

• 70

• 50

• 55

• 68

Multiple Choice

What is the upper quartile?

• 39

• 50

• 55

• 68

Multiple Choice

What is the lower quartile?

• 39

• 40

• 35

• 50

Multiple Choice

What was the median score?

• 39

• 50

• 55

• 16

Multiple Choice

What was the lowest score?

• 20

• 30

• 39

• 40

Making Boxplots in Desmos

I'll now show a short video tutorial on how to do this, then we'll practice using our class data.

Multiple Choice

What is the median height among Math I students?

• 59 in

• 62.5 in

• 67 in

• 69.5 in

• 72

Multiple Choice

How many Math I students are 69.5" or taller?

• 25%

• 50%

• 75%

• 100%

Five Number Summary

A list of the five key values that are shown on a boxplot:

1) Minimum

2) 1st Quartile

3) Median

4) 3rd Quartile

5) Maximum

Shape, Center, Spread

• Shape: look at distance between median and quartiles

• Center: the median

• Spread: Interquartile Range

• IQR = Q3 - Q1

Multiple Choice

What is the interquartile range (IQR)?

• 4

• 64

• 60

• 8

Multiple Choice

Find the interquartile range using the following.

Minimum: 1

Q1: 3

Median: 5

Q3: 7

Maximum: 9

• 8

• 4

• 5

• 10

Comparing Data with Boxplots

Look for key differences between values in their five number summaries (especially median, quartiles, and IQR)

Multiple Choice

Which of the following statements is true?

• The median run times for females is 257.21

• The median run time for males is more than 8 minutes faster than the median run time for females

• The median run times for females is the same as the median run time for males

• There is not enough information to compare the run times for males and females

Multiple Choice

Which squirrels are longer on average?

• Red

• Grey

• They're the same

Multiple Choice

Which group has a larger interquartile range?

• Group A

• Group B

• They're the same

Exit Ticket

Answer the following questions to check your understanding on this lesson's key topics!

Multiple Choice

Which group has a lower IQR?

• Group A

• Group B

Multiple Choice

The box-and-whisker plot displays the number of inches of snowfall last year for 14 cities. Each city had a different amount of snowfall.

What percent of the cities had more than 64 inches of snow?

• 64%

• 50%

• 75%

• 70%

Multiple Choice

The box-and-whisker plot displays the number of inches of snowfall last year for 14 cities. Each city had a different amount of snowfall.

What was the most snowfall that fell on any city?

• 80 inches

• 64 inches

• 69 inches

• 76 inches

Multiple Choice

The middle 50% of scores were between....

• 30-39

• 30-50

• 39-55

• 50-68

Multiple Choice

Which group has a higher median reaction time?

• Group A

• Group B

• They're the same