A random sample of 10 subjects have weights with a standard deviation of 12.5924 kg. What is the variance of their​ weights? Be sure to include the appropriate units with the result.
Question content area bottom
Part 1
The variance of the sample data is 
  
enter your response here 
▼ 
kg cubed .
kg.
kg squared .
​(Round to four decimal places as​ needed.)

To find the variance from the standard deviation, we use the relationship between them:

\[
\text{Variance} = (\text{Standard Deviation})^2
\]

Given that the standard deviation is \( 12.5924 \, \text{kg} \), we can compute the variance as:

\[
\text{Variance} = (12.5924)^2 \, \text{kg}^2
\]

Let's calculate the result.The variance of the sample data is approximately \( 158.5685 \, \text{kg}^2 \) (rounded to four decimal places).

Would you like more details or have any further questions?

Here are some related questions for deeper exploration:
1. What is the formula for calculating variance from a sample set of data?
2. How does variance differ from standard deviation in terms of interpretation?
3. How would you calculate variance if you had the raw data for the weights?
4. Why is variance reported in squared units?
5. What is the role of variance in determining data dispersion?

**Tip:** The variance gives a sense of how spread out data points are from the mean, while the standard deviation gives a more intuitive measure of spread in the same units as the data.

A random sample of 10 subjects have weights with a standard deviation of 12.5924 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.

Learn how to calculate the variance of sample weights given a standard deviation of 12.5924 kg. This problem demonstrates the relationship between variance and standard deviation and provides a step-by-step calculation. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation