Question

use the frequency histogram to complete the following parts. (a) identify the class with the greatest, and the class with the least, relative frequency. (b) estimate the greatest and least relative frequencies. (c) describe any patterns with the data. (a) the class with the greatest relative frequency is □ to □ centimeters. (type integers or decimals. do not round. use ascending order.) the class with the least relative frequency is □ to □ centimeters. (type integers or decimals. do not round. use ascending order.) (b) the greatest relative frequency is about □. (round to two decimal places as needed.) the least relative frequency is about □. (round to two decimal places as needed.)

Explanation:

Step1: Identify greatest relative - frequency class

From the histogram, the class with the greatest relative frequency is the interval with the highest bar. The class with the greatest relative frequency is $38.5 - 40.5$ (since it has the tallest bar among all the classes).

Step2: Identify least relative - frequency class

The class with the least relative frequency is the interval with the shortest non - zero bar. The class with the least relative frequency is $30.5 - 32.5$.

Step3: Estimate relative frequencies

We estimate the relative frequencies by reading the values on the vertical axis for each of the above - identified classes. The relative frequency of the class $38.5 - 40.5$ is approximately $0.22$ (by looking at the height of the bar and estimating from the vertical scale). The relative frequency of the class $30.5 - 32.5$ is approximately $0.04$.

Step4: Analyze patterns

We observe that the data seems to be right - skewed as the tail on the right side (higher values) is longer. The relative frequencies start low, increase to a peak in the $38.5 - 40.5$ class, and then decrease.

Answer:

(a) The class with the greatest relative frequency is $38.5 - 40.5$ to centimeters.
(b) The greatest relative frequency is about $0.22$, and the least relative frequency is about $0.04$.
(c) The data appears to be right - skewed. The relative frequencies increase to a peak in the $38.5 - 40.5$ class and then decrease.