Question

the table shows the battery lives, in hours, of ten brand a batteries and ten brand b batteries.
which would be the best measure of variability to use to compare the data?
only brand a data is symmetric, so standard deviation is the best measure to compare variability.
only brand b data is symmetric, so the median is the best measure to compare variability.
both distributions are symmetric, so the mean is the best measure to compare variability.
both distributions are skewed left, so the interquartile range is the best measure to compare variability.

Explanation:

Step1: Recall the rules for choosing measure of variability

If the data distribution is symmetric, standard deviation is a good measure. If skewed, inter - quartile range is better.

Step2: Check the symmetry of data

For symmetric data, the data is evenly distributed around the center. Looking at Brand A: \(17.0,18.5,19.0,20.0,21.0,22.0,22.5,22.5,23.0,23.0\). For Brand B: \(11.0,12.0,14.0,16.5,17.0,19.5,19.5,20.0,20.5,21.0\). Brand A data is more symmetric (less skewed) compared to Brand B.

Answer:

Only Brand A data is symmetric, so standard deviation is the best measure to compare variability.