In the data set below, what is the variance? 4, 4, 4, 9, 7, 3, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Mean: Calculate the mean of the data set. Mean = (4 + 4 + 4 + 9 + 7 + 3 + 4)/7 μ = 35/7 μ = 5Calculate Sum of Squared Differences: Data set: 4, 4, 4, 9, 7, 3, 4 μ = 5 Calculate the sum of the squared differences from the mean, Σ(x_i - μ)^2. (4 - 5)^2 + (4 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (7 - 5)^2 + (3 - 5)^2 + (4 - 5)^2 = (-1)^2 + (-1)^2 + (-1)^2 + (4)^2 + (2)^2 + (-2)^2 + (-1)^2 = 1 + 1 + 1 + 16 + 4 + 4 + 1 = 28Calculate Variance: We know: Σ(x_i - μ)^2= 28 N= 7 Calculate the variance and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 28/7 σ^2 = 4 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? $\newline$ $4, 4, 4, 9, 7, 3, 4$ $\newline$ 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

4, 4, 4, 9, 7, 3, 4

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Mean: Calculate the mean of the data set. $\newline$ Mean = $(4 + 4 + 4 + 9 + 7 + 3 + 4)/7$ $\newline$ $\mu = 35/7$ $\newline$ $\mu = 5$
Calculate Sum of Squared Differences: Data set: $4, 4, 4, 9, 7, 3, 4$
$\mu = 5$
Calculate the sum of the squared differences from the mean, $\Sigma(x_i - \mu)^2$ .
$(4 - 5)^2 + (4 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (7 - 5)^2 + (3 - 5)^2 + (4 - 5)^2$
$= (-1)^2 + (-1)^2 + (-1)^2 + (4)^2 + (2)^2 + (-2)^2 + (-1)^2$
$= 1 + 1 + 1 + 16 + 4 + 4 + 1$
$= 28$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 28$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 28/7$ $\newline$ $\sigma^2 = 4$ $\newline$ Since the result is not a decimal, there is no need to round.