Measures of Central Tendency/MAD homework Answer Key
Use the following data set to answer the questions. Answers go in the spaces in the table.
Dog height in inches Dog height in inches
12
13.5
11
15
13.5
20
8
6.5
9
24
15
8
18
13.5
20
16
36
19
Mean: 12.06
Median: 12
Mode: none
Range: 13.5
Q
1
: 8.5
Q
3
: 14.25
IQR: 5.75
MAD: 2.97
Mean: 18.83
Median: 18
Mode: none
Range: 28
Q
1
: 14.25
Q
3
: 22
IQR: 7.75
MAD: 5.26
1.
Explain what variability of the data means.
Variability explains how much spread exists in a data set. That means if there many data points far from the mean, the MAD will be high. If most data points are close to the mean, the MAD will be low.
2.
How does MAD explain variability between these two data sets?
The dogs in the first group are closer to the average of 12.06” tall where the dogs in the second group have more variability in height.
Mean Absolute Deviation (MAD).
Example: *Note—this is NOT the answer to your homework!
1) Find the mean of the data set. Mean = 6
2) Subtract the mean from each data point. Use the absolute value of this difference.
3) Find the mean of the new set of data.
In explaining the MAD, remember to use the word “variation” or “spread”