Consider the following data:

−13,9,9,−13,5,−13,9

Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place.


To calculate the sample variance, we follow these steps:

### Step 1: Calculate the mean of the sample

The data set is:  
\(-13, 9, 9, -13, 5, -13, 9\)

The formula for the mean \(\bar{x}\) is:
\[
\bar{x} = \frac{\sum x_i}{n}
\]
where \(x_i\) represents each data point and \(n\) is the number of data points.

\[
\bar{x} = \frac{-13 + 9 + 9 + (-13) + 5 + (-13) + 9}{7}
\]

### Step 2: Calculate the squared differences from the mean

For each data point, subtract the mean and square the result.

### Step 3: Compute the sample variance

The formula for sample variance \(s^2\) is:
\[
s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}
\]
Let me calculate this.The value of the sample variance is \(128.0\), rounded to one decimal place.

Do you want more details or have any questions?

Here are 5 related questions you might find useful:
1. How do you calculate the standard deviation from variance?
2. What is the difference between sample variance and population variance?
3. Why do we divide by \(n - 1\) for sample variance instead of \(n\)?
4. Can the sample variance ever be negative?
5. How does the sample variance change if all data points increase by a constant value?

**Tip:** The square root of the variance gives the standard deviation, which is a measure of how spread out the numbers are in the sample.

Consider the following −13, 9, 9, −13, 5, −13, 9. Step 1 of 3: Calculate the value of the sample variance. Round your answer to one decimal place.

Learn how to calculate the sample variance for the data set -13, 9, 9, -13, 5, -13, 9. This solution walks through the process of finding the mean and applying the sample variance formula step-by-step. Suitable for students in Grades 9-12 studying statistics and probability.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation