Question

(a) the class with the greatest relative frequency is 38.5 to 40.5 centimeters. (type integers or decimals. do not round. use ascending order.) (b) the greatest relative frequency is about 0.22. (round to two decimal places as needed.) (c) describe any patterns with the data. (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.

Explanation:

Step1: Identify greatest relative - frequency class

From the bar - chart, we observe the height of the bars representing relative frequencies. The class with the greatest relative frequency is the one with the tallest bar. Looking at the chart, the class with lengths from 40.5 to 42.5 centimeters has the greatest relative frequency.

Step2: Identify least relative - frequency class

The class with the least relative frequency is the one with the shortest bar. From the chart, the class with lengths from 30.5 to 32.5 centimeters has the least relative frequency.

Step3: Estimate greatest and least relative frequencies

We estimate the values from the y - axis (relative frequency axis). The greatest relative frequency (for the 40.5 - 42.5 class) is approximately 0.22 (as given in the problem statement). The least relative frequency (for the 30.5 - 32.5 class) is approximately 0.05.

Step4: Describe patterns

The pattern shows that the relative frequencies are not evenly distributed. There is a peak in the middle - length classes (around 40.5 - 42.5 centimeters) and lower frequencies at the extreme ends (shorter and longer lengths).

Answer:

(a) The class with the greatest relative frequency is 40.5 to 42.5 centimeters.
(b) The greatest relative frequency is about 0.22, and the least relative frequency (for the class 30.5 to 32.5 centimeters) is about 0.05.
(c) The pattern is that relative frequencies are higher in the middle - length classes and lower at the extreme lengths.