Question

the table shows the battery lives, in hours, of ten brand a batteries and ten brand b batteries.
battery life (hours)

brand a	22.5	17.0	21.0	23.0	22.0	18.5	22.5	20.0	19.0	23.0
brand b	20.0	19.5	20.5	16.5	14.0	17.0	11.0	19.5	21.0	12.0

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:

When data is symmetric, the standard - deviation is a good measure of variability. When data is skewed, the inter - quartile range is a better measure. By looking at the data values of Brand A and Brand B, Brand A seems more symmetric while Brand B has some lower extreme values (11.0, 12.0, 14.0) which makes it skewed left. The inter - quartile range is robust to outliers and skewness.

Answer:

Both distributions are skewed left, so the interquartile range is the best measure to compare variability.