In the data set below, what is the variance? 4, 6, 7, 1, 8, 7 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now, let's calculate the squared differences from the mean. (4 - 5.5)^2 + (6 - 5.5)^2 + (7 - 5.5)^2 + (1 - 5.5)^2 + (8 - 5.5)^2 + (7 - 5.5)^2 = (-1.5)^2 + (0.5)^2 + (1.5)^2 + (-4.5)^2 + (2.5)^2 + (1.5)^2 = 2.25 + 0.25 + 2.25 + 20.25 + 6.25 + 2.25 = 33.5Find 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) = 33.5 / 6 Variance (σ^2) = 5.583333... Rounded to the nearest tenth, the variance is 5.6

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? $\newline$ $4, 6, 7, 1, 8, 7$ $\newline$ 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

4, 6, 7, 1, 8, 7

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now, let's calculate the squared differences from the mean. $\newline$ $(4 - 5.5)^2 + (6 - 5.5)^2 + (7 - 5.5)^2 + (1 - 5.5)^2 + (8 - 5.5)^2 + (7 - 5.5)^2$ $\newline$ = $(-1.5)^2 + (0.5)^2 + (1.5)^2 + (-4.5)^2 + (2.5)^2 + (1.5)^2$ $\newline$ = $2.25 + 0.25 + 2.25 + 20.25 + 6.25 + 2.25$ $\newline$ = $33.5$
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 $\sigma^2$ = $\frac{33.5}{6}$ $\newline$ Variance $\sigma^2$ = $5$ . $583333$ ... $\newline$ Rounded to the nearest tenth, the variance is $5.6$