Question

are you ready for more? 1 these two box plots have the same median and the same iqr. how could we compare the variability of the two distributions? 2 these two dot plots have the same mean and the same mad. how could we compare the variability of the two distributions? lesson summary the mean absolute deviation, or mad, is a measure of variability that is calculated by finding the mean distance from the mean of all the data points. here are two dot plots, each with a mean of 15 centimeters, displaying the length of sea scallop shells in centimeters.

Explanation:

Step1: Recall variability measures

Since common measures like median, IQR, mean and MAD are already equal, we can look at range.

Step2: Define range

The range is the difference between the maximum and minimum values in a data - set. A larger range indicates greater variability.

Step3: Consider spread of data points

We can also look at how spread out the data points are relative to each other. For example, in a dot - plot, if the dots are more clustered around the mean in one distribution compared to the other, the less clustered one has more variability. In a box - plot, we can look at the length of the whiskers. Longer whiskers may indicate greater variability.

Answer:

1. Calculate the range for each distribution (maximum value - minimum value). A larger range implies greater variability.
2. Examine the spread of data points. In a dot - plot, check how clustered or dispersed the dots are. In a box - plot, look at the length of the whiskers; longer whiskers suggest more variability.