Question

The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58


What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.

Answer 1

(d) The IQR is the best measure of variability, and it equals 18.5.

Explanation:

You want to know the best measure of variability for the data in the given stem-and-leaf plot.

• 0 | 5
• 1 | 0, 3, 7
• 2 | 4, 6, 8
• 3 | 2
• 4 |
• 5 | 8

Statistics

The attachment shows the values of interest are ...

Range = 58 -5 = 53

IQR = 30 -11.5 = 18.5

Measure of variability

You can see from the shape of the stem-and-leaf plot that the mean and median are near 24, and most of the data is clustered in that neighborhood. The outlier at 58 skews the distribution to the right.

Since the data has an outlier, we choose the IQR as a better measure of the variability than the range is.

The IQR is the best measure of variability, and it equals 18.5.

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Additional comment

Neither the IQR nor the range is 45. The range is definitely not 18.5. This means the answer choice we have selected is the only true statement about the data set. (It will often be the case that the only answer that is a true statement is the correct answer.)

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