At least one of your answers is incorrect. The​ variance, 

s squareds2​, 

of a set of values is a measure of variation equal to the square of the standard deviation. The units of the variance are the squares of the units of the original data values. Remember to round to four decimal places.

You're correct that the variance is equal to the square of the standard deviation, and the units should indeed be the square of the original units. Let's correct the calculation and ensure that it's rounded to four decimal places.

Given:
- Standard deviation (\( s \)) = 13.2965 kg

To find the variance (\( s^2 \)), square the standard deviation:

\[
s^2 = (13.2965 \, \text{kg})^2 = 176.75026425 \, \text{kg}^2
\]

Now, rounding this to four decimal places:

\[
s^2 = 176.7503 \, \text{kg}^2
\]

So, the correct variance of the sample data is **176.7503 kg²**.

Would you like further details or have any questions?

Here are 5 related questions:
1. Why is it important to round to a specific number of decimal places in statistics?
2. How would you calculate the standard deviation if only the variance is provided?
3. What would the variance be if the standard deviation were doubled?
4. How does sample size affect the variance?
5. What is the difference between sample variance and population variance?

**Tip:** Always double-check your rounding to ensure accuracy, especially in statistical calculations!

Explore the concept of variance in statistics, its calculation, and significance. Learn how variance is derived from the square of the standard deviation with an example. Suitable for college-level students and those interested in statistical analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation