Questions: A random sample of 10 subjects have weights with a standard deviation of 10.2333 kg. What is the variance of their weights? Be sure to include the appropriate units with the result. The variance of the sample data is (Round to four decimal places as needed.)

A random sample of 10 subjects have weights with a standard deviation of 10.2333 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.

The variance of the sample data is
(Round to four decimal places as needed.)

Transcript text: A random sample of 10 subjects have weights with a standard deviation of 10.2333 kg . What is the variance of their weights? Be sure to include the appropriate units with the result The variance of the sample data is $\square$ $\square$ (Round to four decimal places as needed.)

Solution

Solution Steps

Step 1: Understand the Problem

We are given the standard deviation ($\sigma$) of a sample data set and the size of the sample ($n$). Our goal is to find the variance ($\sigma^2$) of this sample data set.

Step 2: Apply the Formula

The variance ($\sigma^2$) is calculated by squaring the standard deviation ($\sigma$). The formula to find the variance from the standard deviation is: \[ \sigma^2 = \sigma \times \sigma \]

Step 3: Substitute the Values and Calculate

Given that the standard deviation ($\sigma$) is 10.233, we substitute it into the formula: \[ \sigma^2 = 10.233 \times 10.233 \] This gives us a variance ($\sigma^2$) of 104.720.