Answer:
D. The standard deviation is the best measure because both data distributions are symmetric.
Step-by-step explanation:
We have been given two box plots which show the distributions of weights of cucumbers and zucchini collected from a garden.
Since we know that the most common measures of variability of spread are range, inter-quartile range, variance and standard deviation.
Let us see our given options one by one to choose the correct option.
A. The mean is the best measure because the data sets have the same minimum weight.
Since the mean is a measure for the central tendency of a data set, therefore, option A in not true about the measure of variability.
B. The range is the best measure because the distribution of zucchini weights is skewed left.
We can see that both of our box plots are symmetric, therefore, option B is not true.
C. The median is the best measure because the data sets have different medians.
Median is the measure of central tendency of a data set. It is not a measure of variability, therefore, option C is not true.
D. The standard deviation is the best measure because both data distributions are symmetric.
Since both of our given box plots are symmetric and standard deviation is the best measure for symmetric data sets, therefore, option D is the correct choice.
