Question

a. what is the range of each group?
b. which group had the larger standard deviation? explain.

1. the mean of a distribution of selected homecoming dresses is $95 with a standard deviation of $15. the mean of a distribution of homecoming shoes is $28 with a standard deviation of $10.

which distribution has the lower standard deviation?
which distribution is more spread out? explain.

Explanation:

Step1: Recall range formula

Range = Maximum - Minimum

Step2: Analyze home - coming dresses

For home - coming dresses, no data about maximum and minimum is given to calculate range. But for standard deviation comparison, standard deviation of home - coming dresses is $\sigma_{dresses}= 15$

Step3: Analyze home - coming shoes

Standard deviation of home - coming shoes is $\sigma_{shoes}=10$

Step4: Compare standard deviations

Since $15>10$, the distribution of home - coming dresses has a larger standard deviation and is more spread out.

Answer:

The distribution of home - coming dresses has a larger standard deviation and is more spread out because its standard deviation is $15$ while the standard deviation of home - coming shoes is $10$.