This document provides definitions and examples of interquartile range (IQR) and mean absolute deviation (MAD) as measures of variability. It then has students calculate the IQR and MAD for two data sets, data sets A and B, which contain heights. The IQR is greater for data set B, indicating a wider spread in the middle half of heights. The MAD is also greater for data set B, showing heights in B are generally farther from the mean than those in A.

1. Name ___________________________________ Date __________________
Mrs. Labuski / Mrs. Portsmore Period __________ Unit 12 Lesson 5B Measure of
Variability OC 7-3
VOCABULARY DEFINITION EXAMPLE
interquartile
range (IQR)
a measure of variability.
the difference of the upper
quartile and the lower quartile.
see below
mean
absolute
deviation
(MAD)
Another measure of variability.
The mean distance between each
data value and the mean of the
data set.
see below
Find the IQR for the data sets from yesterday’s notes.
A.
B.
Find the IQR for the data sets.
A IQR = Upper quartile – Lower quartile =
61.5 – 57 = 4.5
B IQR = Upper quartile – Lower quartile =
52 – 46 = 6
Compare the IQRs. How do the IQRs describe the distribution of the heights in each group?
The IQR in B is greater; the heights in the middle half of B are more spread out than in
A.

2. Find the MAD for the data sets in A.
60, 58, 54, 56, 63, 61, 65, 61, 62, 59, 56, 58
Step 1 Find the mean. Round to the nearest whole number.
Step 2 Complete the table.
Step 3 To calculate the MAD, find the mean of the values in the second row of the table. Round
to the nearest whole number.

3. Find the MAD for the data sets in B.
46, 47, 48, 48, 56, 48, 46, 52, 57, 52, 45
Step 1 Find the mean. Round to the nearest whole
number.
Step 2 Complete the table.
Step 3 To calculate the MAD, find the mean of the values in the second row of the table. Round
to the nearest whole number.
Compare the MADs. How do the MADs describe the distribution of the heights in each group?
The MAD in B is greater; in general, the heights in B are farther from the mean than the
heights in A.

4. Name ___________________________________ Date __________________
Mrs. Labuski / Mrs. Portsmore Period __________ Unit 12 Lesson 5B Measure of
Variability OC 7-3
VOCABULARY DEFINITION EXAMPLE
interquartile
range (IQR)
see below
mean
absolute
deviation
(MAD)
see below
Find the IQR for the data sets from yesterday’s notes.
A.
B.
A IQR = Upper quartile – Lower quartile =
___________ – ___________ = ___________
B IQR = Upper quartile – Lower quartile =
___________ – ___________ = ___________
Compare the IQRs. How do the IQRs describe the distribution of the heights in each group?
_____________________________________________________________________________
_____________________________________________________________________________

5. Find the MAD for the data sets in A.
60, 58, 54, 56, 63, 61, 65, 61, 62, 59, 56, 58
Step 1 Find the mean. Round to the nearest whole number.
Step 2 Complete the table.
Step 3 To calculate the MAD, find the mean of the values in the second row of the table. Round
to the nearest whole number.

6. Find the MAD for the data sets in B.
46, 47, 48, 48, 56, 48, 46, 52, 57, 52, 45
Step 1 Find the mean. Round to the nearest whole number.
Step 2 Complete the table.
Step 3 To calculate the MAD, find the mean of the values in the second row of the table.
Round to the nearest whole number.
Compare the MADs. How do the MADs describe the distribution of the heights in each group?
_____________________________________________________________________________
_____________________________________________________________________________