In the data set below, what is the variance? 6, 4, 1, 9, 7, 9 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Data Set: Data set: 6, 4, 1, 9, 7, 9 μ = 6 Calculate the sum of the squared differences from the mean. (6 - 6)^2 + (4 - 6)^2 + (1 - 6)^2 + (9 - 6)^2 + (7 - 6)^2 + (9 - 6)^2 = (0)^2 + (-2)^2 + (-5)^2 + (3)^2 + (1)^2 + (3)^2 = 0 + 4 + 25 + 9 + 1 + 9 = 48Calculate Sum: We have the sum of the squared differences: Σ(x_i - μ)^2= 48 The number of data points N= 6 Calculate the variance and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 48/6 σ^2 = 8 Since the result is not a decimal, there is no need to round.

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? $\newline$ $6, 4, 1, 9, 7, 9$ $\newline$ 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

6, 4, 1, 9, 7, 9

\newline

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

\newline

variance

(\sigma^2)

: _____

Data Set: Data set: $6, 4, 1, 9, 7, 9$ $\newline$ $\mu = 6$ $\newline$ Calculate the sum of the squared differences from the mean. $\newline$ $(6 - 6)^2 + (4 - 6)^2 + (1 - 6)^2 + (9 - 6)^2 + (7 - 6)^2 + (9 - 6)^2$ $\newline$ $= (0)^2 + (-2)^2 + (-5)^2 + (3)^2 + (1)^2 + (3)^2$ $\newline$ $= 0 + 4 + 25 + 9 + 1 + 9$ $\newline$ $= $48$
Calculate Sum: We have the sum of the squared differences:$\newline$$\Sigma(x_i - \mu)^2= 48$$\newline$The number of data points $N= 6$$\newline$Calculate the variance and round your answer to the nearest tenth.$\newline$$\sigma^2 = (\Sigma(x_i - \mu)^2)/N$$\newline$$\sigma^2 = 48/6$$\newline$$\sigma^2 = 8$$\newline$Since the result is not a decimal, there is no need to round.