Question
Maria surveyed girls on the amount (in $) they spent on a dress for the middle school spring fling:
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 skewed
IQR; the data distribution is skewed
MAD; the data distribution has outliers
MAD; the data distribution has outliers
IQR; the data distribution is symmetrical
IQR; the data distribution is symmetrical
MAD; the data distribution is symmetrical
IQR; the data distribution is skewed
To determine the best measure of variability to describe the spread of the dataset, we can consider the characteristics of the data distribution.
Looking at the dataset provided, we can see that the values are not evenly distributed and there may be some outliers present.
The interquartile range (IQR) is a measure of variability that focuses on the middle 50% of the data and is not influenced by outliers. It provides information about the spread of the central portion of the dataset.
On the other hand, the mean absolute deviation (MAD) is a measure of variability that calculates the average distance between each data point and the mean. It gives equal weight to all the data points, including outliers.
Based on the characteristics of the dataset, the best measure of variability would be MAD because the data distribution has outliers.
Therefore, the correct answer is:
MAD; the data distribution has outliers.