In the data set below, what is the variance? 2, 9, 6, 8, 8, 4, 5 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Variance: Now, let's do the variance thing. We need to sum up each (number - mean)^2. So, (2 - 6)^2 + (9 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (8 - 6)^2 + (4 - 6)^2 + (5 - 6)^2 That's (-4)^2 + (3)^2 + (0)^2 + (2)^2 + (2)^2 + (-2)^2 + (-1)^2 Which is 16 + 9 + 0 + 4 + 4 + 4 + 1 Sum = 38Sum of Squares: Finally, divide that sum by the number of data points to get the variance. Variance = Sum / 7 Variance = 38 / 7 Variance = 5.428571... Round it to the nearest tenth and we get 5.4

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? $\newline$ $2, 9, 6, 8, 8, 4, 5$ $\newline$ 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, 9, 6, 8, 8, 4, 5

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Variance: Now, let's do the variance thing. $\newline$ We need to sum up each $(\text{number} - \text{mean})^2$ . $\newline$ So, $(2 - 6)^2 + (9 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (8 - 6)^2 + (4 - 6)^2 + (5 - 6)^2$ $\newline$ That's $(-4)^2 + (3)^2 + (0)^2 + (2)^2 + (2)^2 + (-2)^2 + (-1)^2$ $\newline$ Which is $16 + 9 + 0 + 4 + 4 + 4 + 1$ $\newline$ Sum = $38$
Sum of Squares: Finally, divide that sum by the number of data points to get the variance. $\newline$ $\text{Variance} = \frac{\text{Sum}}{7}$ $\newline$ $\text{Variance} = \frac{38}{7}$ $\newline$ $\text{Variance} = 5.428571\ldots$ $\newline$ Round it to the nearest tenth and we get $5.4$