Maria surveyed girls on the amount (in $) they spent on a dress for the middle school spring fling:

Question

79, 79, 79, 82, 84, 85, 89, 90, 99, 100, 100, 100, 129, 139, 155, 174, 189, 200, 209, 250

Which measure of variability—IQR or MAD—best describes the spread of the dataset?

(1 point)
Responses

IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical

MAD; the data distribution is symmetrical
MAD; the data distribution is symmetrical

MAD; the data distribution has outliers
MAD; the data distribution has outliers

IQR; the data distribution is skewed

Answer 1

To determine which measure of variability—Interquartile Range (IQR) or Mean Absolute Deviation (MAD)—best describes the spread of the dataset, we need to analyze the dataset and its characteristics.

1. Identifying Outliers and the Distribution:

   • The values in the dataset range from 79 to 250, with several high values that may indicate potential outliers (especially the 200 and 250).
   • The presence of high values (200, 209, 250) suggests that the data distribution may be skewed.

2. Checking for Skewness:

   • When there are outliers or extreme values in the dataset, it is often best to use the IQR rather than MAD, as IQR is more robust to outliers and better suited for skewed distributions.

3. Conclusion:

   • Given that the data distribution appears to be skewed due to the presence of outliers, the IQR is the more appropriate measure of variability.

Thus, the best answer is:

IQR; the data distribution is skewed.