In the data set below, what is the variance? 9, 6, 7, 7, 9, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Data Set: Data set: 9, 6, 7, 7, 9, 4 μ = 7 Calculate the sum of the squared differences from the mean. Σ(x_i - μ)^2 = (9 - 7)^2 + (6 - 7)^2 + (7 - 7)^2 + (7 - 7)^2 + (9 - 7)^2 + (4 - 7)^2 = (2)^2 + (-1)^2 + (0)^2 + (0)^2 + (2)^2 + (-3)^2 = 4 + 1 + 0 + 0 + 4 + 9 = 18Calculate Sum: We have: Σ(x_i - μ)^2= 18 N= 6 Now, calculate the variance using the formula and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 18/6 σ^2 = 3 Since the result is a whole number, there is no need to round to the nearest tenth.

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? $\newline$ $9, 6, 7, 7, 9, 4$ $\newline$ 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

9, 6, 7, 7, 9, 4

\newline

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

\newline

variance

(\sigma^2)

: _____

Data Set: Data set: $9, 6, 7, 7, 9, 4$ $\newline$ $\mu = 7$ $\newline$ Calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \mu)^2 = (9 - 7)^2 + (6 - 7)^2 + (7 - 7)^2 + (7 - 7)^2 + (9 - 7)^2 + (4 - 7)^2$ $\newline$ $= (2)^2 + (-1)^2 + (0)^2 + (0)^2 + (2)^2 + (-3)^2$ $\newline$ $= 4 + 1 + 0 + 0 + 4 + 9$ $\newline$ $= 18$
Calculate Sum: We have: $\newline$ $\Sigma(x_i - \mu)^2= 18$ $\newline$ $N= 6$ $\newline$ Now, calculate the variance using the formula and round your answer to the nearest tenth. $\newline$ $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 18/6$ $\newline$ $\sigma^2 = 3$ $\newline$ Since the result is a whole number, there is no need to round to the nearest tenth.