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

Subtract and Square: Now, subtract the mean from each number and square the result. (2 - 4)^2 + (4 - 4)^2 + (9 - 4)^2 + (3 - 4)^2 + (4 - 4)^2 + (2 - 4)^2 + (4 - 4)^2 = (-2)^2 + (0)^2 + (5)^2 + (-1)^2 + (0)^2 + (-2)^2 + (0)^2 = 4 + 0 + 25 + 1 + 0 + 4 + 0 = 34Calculate Sum: Finally, divide by the number of data points minus 1 to get the sample variance. σ^2 = 34 / (7 - 1) σ^2 = 34 / 6 σ^2 = 5.666... Round to the nearest tenth. σ^2 ≈ 5.7

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? $\newline$ $2, 4, 9, 3, 4, 2, 4$ $\newline$ 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

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

\newline

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

\newline

variance

(\sigma^2)

: _____

Subtract and Square: Now, subtract the mean from each number and square the result. $\newline$ (2 - 4)^2 + (4 - 4)^2 + (9 - 4)^2 + (3 - 4)^2 + (4 - 4)^2 + (2 - 4)^2 + (4 - 4)^2$\newline= (-2)^2 + (0)^2 + (5)^2 + (-1)^2 + (0)^2 + (-2)^2 + (0)^2 $\newline$ = 4 + 0 + 25 + 1 + 0 + 4 + 0 $\newline$ = 34$
Calculate Sum: Finally, divide by the number of data points minus $1$ to get the sample variance. $\newline$ $\sigma^2 = \frac{34}{(7 - 1)}$ $\newline$ $\sigma^2 = \frac{34}{6}$ $\newline$ $\sigma^2 = 5.666...$ $\newline$ Round to the nearest tenth. $\newline$ $\sigma^2 \approx 5.7$