A random sample of 10 subjects have weights with a standard deviation of 12.4397 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 
select: 154.6767 
154.6767 
kg squared .
​(Round to four decimal places as​ needed.)

To calculate the variance of the weights, we use the relationship between standard deviation and variance. The variance (\( \sigma^2 \)) is simply the square of the standard deviation (\( \sigma \)).

Given:
- Standard deviation \( \sigma = 12.4397 \) kg

The variance is:
\[
\text{Variance} = \sigma^2 = (12.4397)^2
\]

Now, let's compute that:

\[
\text{Variance} = 154.6767 \, \text{kg}^2
\]

Thus, the variance of the sample data is \( 154.6767 \, \text{kg}^2 \), rounded to four decimal places.

Would you like more details on how variance and standard deviation are related or need further clarification?

Here are 5 related questions you might find helpful:
1. What is the formula for variance and how does it differ from standard deviation?
2. How does sample size affect variance and standard deviation?
3. What are some real-world examples where understanding variance is useful?
4. How do you interpret variance in the context of weight data?
5. Can you explain the difference between population variance and sample variance?

**Tip:** Always double-check whether you're working with a sample or population, as the formulas for variance slightly differ.

A random sample of 10 subjects have weights with a standard deviation of 12.4397 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 a random sample's weight data from the standard deviation of 12.4397 kg. The problem explains the relationship between variance and standard deviation, with a step-by-step solution. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation