Whiskers Plot Math

Box and Whisker Plots

What a Box and Whisker Plot look like?

Get it!!!

What does a Box and Whisker Plot includes?

Other Names:

Lower Extreme = Least Value = Minimum

Lower Quartile = First Quartile = Q1

Median = Q2

Upper Quartile = Third Quartile = Q3

Upper Extreme = Greatest Value = Maximum

Multiple Choice

Which has a Median of 1?

• Zach 
• Steven 
• They both have a median on 1

Multiple Choice

Which city has skewed right spread?

• Millersburg

• Arcadia

Multiple Choice

What is the overall shape of the graph?

• Approximately Symmetrical

• Skewed Left

• Skewed Right

Multiple Choice

What is the overall shape of the graph?

• Approximately Symmetrical

• Skewed left

• Skewed right

Range and Interquartile Range Formulas

Range = Maximum # - Minimum #

(Upper Extreme - Lower Extreme)

Interquartile Range (IQR) = Q3 -Q1

Outliers

An outlier is a number in a data set that is very different from the rest of the numbers.

It can have a MAJOR effect on the mean.

Example 5: Find Outliers

Find the outliers for the following data set.

{35,16,17,17,19,9}

How to find Outliers using 1.5 IQR rule

Step 1: IQR X 1.5

Step 2: Q1 - (IQR X 1.5)

Step 3: Q3 + (IQR X 1.5)

Any number in the data set that is below or above these numbers are outliers.

Multiple Choice

Use the 1.5 IQR rule to determine if there are any outliers for the following numbers:

84, 88, 72, 74, 98, 35, 94

• Yes, 35 is an outlier.

• Yes, 33 is an outlier.

• Yes, 98 is an outlier.

• There are no numbers less than 39 or greater than 124, therefore there are no outliers.

Multiple Choice

What is the Range of this data set?

• 13

• 37

• 72

Multiple Choice

Which has a larger IQR?

• Zach
• Steven
• They have the same IQR

Multiple Choice

What is the Interquartile Range of this data set? The lower (first) quartile is 19 and the upper (3rd) quartile is 56.

• 75

• 37

• 72

Multiple Choice

Which box and whisker plot has an upper extreme of 100?

• Plot 1

• Plot 2

• Plot 3

• Plot 4

Multiple Choice

Which plot has a median of 50?

• Plot 1

• Plot 2

• Plot 3

• Plot 4

Multiple Choice

Which is NOT ture?

• The spreads of the low temperatures for Reybold and Picktown are not the same
• Neither box plot is symmetrical
• The median low temeratures for Reybold and Picktown are different
• The lower extreme for Picktown is approximately 5 degrees lower than the lower extreme for Reybold

Example 2: Find 5 Number Summary

Find the 5 Number Summary for the following data set.

{8,6,3,5,3,4,2,9}

Example 3: Draw a Box and Whisker Plot

Draw a Box and Whisker Plot for the following data set.

{9,7,4,5,3,4,2}

Multiple Choice

What is the Q1 of this data set?

6, 7, 2, 1, 5, 2, 1, 6

• 1

• 1.5

• 2

• 2.5

Multiple Choice

What is the Q3 of this data set?

6, 7, 2, 1, 5, 2, 1, 6

• 5

• 6

• 5.5

• 6.5

Multiple Choice

Identify the median for the given data?

23, 34, 27, 7, 30, 26, 28, 31, 34

• 28

• 23

• 31

• 34

Multiple Choice

When finding median and the middle has two numbers instead of one, what do you do?

• Take the higher number

• Take the lower number

• Take both

• Take the average

Multiple Choice

Which of the following lists all parts of the five number summary?

• Mean, Median, Mode, Range, and Total

• Minimum, Quartile 1, Median, Quartile 3, and Maximum

• Smallest, Q1, Q2, Q3, and Q4

• Minimum, Maximum, Range, Mean, and Median

Multiple Choice

What do points A and E represent on the box plot?

• Mean and Mode

• Mean and Median

• Least and Greatest Value

• First and Third Quartiles

How is a Box and Whisker Plot set up?

You have 4 different section.

Each section is worth 25%.

It does not matter if each section are not the same size.

Example 1: Find the percentage.

What is the percentage of the data are each of the following sections?

Section 1=?

Sections 1 and 2=?

Sections 3 and 4=?

Sections 1, 2, and 3=?

Multiple Choice

What percent of the data is between 25 and 30 on the number line?

• 25%

• `50%

• 75%

• 100%

Multiple Choice

What percentage of the data is between 90 and 140?

• 25 %

• 50%

• 75%

• 100%

Multiple Choice

Range is

• the difference between the third quartile and the first quartile

• the difference between the greatest and least data values.

Multiple Choice

Interquartile Range is

• the difference between the third quartile and the first quartile

• the difference between the greatest and least data values.

Multiple Choice

What is the range of this data set?

• 6

• 12

• 13

• 19

Multiple Choice

What is the median of this data set?

• 8

• 12

• 15

• 19

Multiple Choice

What do points A and E represent on the box plot?

• Mean and Mode

• Mean and Median

• Least and Greatest Value

• First and Third Quartiles

Multiple Choice

What do points B and D represent on the box plot?

• Mean and Mode

• Mean and Median

• Least and Greatest Value

• First and Third Quartiles

Multiple Choice

What does point C on the box plot represent?

• First Quartile

• Median

• Third Quartile

• Mean

Multiple Choice

What percentage of the data is between 40 and 150?

• 25 %
• 50%
• 75%
• 100%

Multiple Choice

What percent of students have heights between 60 inches and 66 inches?

• 75%
• 50%
• 100%
• 25%

Multiple Choice

11. What percentage of the data is between 90 and 140?

• 25 %
• 50%
• 75%
• 100%

Multiple Choice

What percent of the data is between 25 and 30 on the number line?

• 25%
• `50%
• 75%
• 100%