In the data set below, what is the variance? 3, 7, 9, 7, 4, 2, 3 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. Σ(x_i - mean)^2 = (3 - 5)^2 + (7 - 5)^2 + (9 - 5)^2 + (7 - 5)^2 + (4 - 5)^2 + (2 - 5)^2 + (3 - 5)^2 Σ(x_i - mean)^2 = (-2)^2 + (2)^2 + (4)^2 + (2)^2 + (-1)^2 + (-3)^2 + (-2)^2 Σ(x_i - mean)^2 = 4 + 4 + 16 + 4 + 1 + 9 + 4 Σ(x_i - mean)^2 = 42Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. Variance (σ^2) = Σ(x_i - mean)^2 / N Variance (σ^2) = 42 / 7 Variance (σ^2) = 6

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In the data set below, what is the variance? $\newline$ $3, 7, 9, 7, 4, 2, 3$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

View step-by-step help

Home

Math Problems

Algebra 1

Variance and standard deviation

Full solution

Q. In the data set below, what is the variance?

\newline

3, 7, 9, 7, 4, 2, 3

\newline

If the answer is a decimal, round it to the nearest tenth.

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \text{mean})^2 = (3 - 5)^2 + (7 - 5)^2 + (9 - 5)^2 + (7 - 5)^2 + (4 - 5)^2 + (2 - 5)^2 + (3 - 5)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = (-2)^2 + (2)^2 + (4)^2 + (2)^2 + (-1)^2 + (-3)^2 + (-2)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 4 + 4 + 16 + 4 + 1 + 9 + 4$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 42$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{42}{7}$ $\newline$ Variance $\sigma^2$ = $6$