Module 2 Lesson 7: Measuring Variability for Skewed Distributions

(Interquartile Range)

Warm Up:

Calculate the mean and median for the following set of data: 15, 21, 19, 33, 46, 31, 22, 11

Mean:

Median:

Example 1

1. Put a mark underneath the dot

plot to show the approximate mean.

2. What is the direction of the tail?

3. How does this tail affect the

mean?

4. The mean is about 50. Does that

seem like a typical age for a viewer?

Using the above dot plot, construct a box plot over the dot plot by completing

the following steps:

i. Locate the middle 40 observations, and draw a box around these values.

ii. Calculate the median, and then draw a line in the box at the location of the

median.

iii. Draw a line that extends from the upper end of the box to the largest

observation in the data set.

iv. Draw a line that extends from the lower edge of the box to the minimum

value in the data set.

Steps to Create a Box Plot

A quartile is the

“median of each

side of the median”

A helps us to describe the 5 number summary

shape of a box plot. Complete a 5 number

summary for the viewer example above.

1. What percent of the data is shown in the box

(the interquartile range)?

2. What percent of the data is shown in each

“whisker”?

Example 2

This box plot shows the age of 200 people in

Kenya.

1. Complete a 5 number summary for the data.

2. What do you think that the * are?

3. What are the minimum values for an outlier?

An outlier is defined to be any data value

that is more than 1.5×(𝐼𝑄𝑅) away from the

nearest quartile.

Exit Ticket

Given the data from your warm up: 15, 21, 19, 33, 46, 31, 22, 11

1. Create a dot plot for the data.

2. Complete a 5 number summary for the data.

3. Create a box plot.