Calculate the sample variance and sample standard deviation for the following frequency distribution of heights in centimeters for a sample of 8-year-old boys. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heights in Centimeters Class Frequency 116.1 - 120.0 38 120.1 - 124.0 24 124.1 - 128.0 28 128.1 - 132.0 43 132.1 - 136.0 29

--- sample variance

--- sample standard deviation

Step-by-step explanation:

Given

Required

Calculate the sample variance and sample standard deviation

First, we calculate the midpoint of each class:

The midpoints are calculated by taking the average of the class intervals.

For instance:

Class 116.1 to 120.0 has a midpoint of

The same approach is applied to other classes.

Next, is to calculate the mean:

In this case, it is:

Where

So, we have:

The sample variance (s^2) is:

This gives:

The sample standard deviation (s) is: