Question

For a sample of 10 cities, the mean robbery rate is 144 with a standard deviation of 110; the mean aggravated assault rate is 160 with a standard deviation of 90. Which offense has greater variability?

Answer 1

The robbery offense has greater variability as its standard deviation of 110 is higher than that of the aggravated assault rate, which has a standard deviation of 90.

Step-by-step explanation:

To determine which offense has greater variability, we look at the standard deviation of the robbery rate and aggravated assault rate. Variability is indicated by how much the data points differ from the mean, and standard deviation is a measure of that variability.

Here, the robbery rate has a mean of 144 and a standard deviation of 110, while the aggravated assault rate has a mean of 160 and a standard deviation of 90.

Even though the standard deviation can be greater than the average, as in the case of the robbery rate, it simply means that the data points are spread out widely around the mean. When the standard deviation is a large part of the mean, like in the robbery rate example, it suggests that there is a high level of variability, with some cities having much higher or much lower robbery rates than the average.

In this instance, because the standard deviation of the robbery rate (110) is greater than that of the aggravated assault rate (90), we can conclude that the robbery offense has greater variability among the 10 cities sampled.