In the data set below, what is the variance? 1, 9, 9, 9, 7, 4, 3 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 = (1 + 9 + 9 + 9 + 7 + 4 + 3)/7 μ = 42/7 μ = 6Calculate Sum of Squared Differences: Data set: 1, 9, 9, 9, 7, 4, 3 μ = 6 Calculate the sum of the squared differences from the mean. (1 - 6)^2 + (9 - 6)^2 + (9 - 6)^2 + (9 - 6)^2 + (7 - 6)^2 + (4 - 6)^2 + (3 - 6)^2 = (-5)^2 + (3)^2 + (3)^2 + (3)^2 + (1)^2 + (-2)^2 + (-3)^2 = 25 + 9 + 9 + 9 + 1 + 4 + 9 = 66Calculate Variance: We have: Σ(x_i - μ)^2= 66 N= 7 Calculate the variance and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 66/7 σ^2 ≈ 9.4 when rounded 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? $\newline$ $1, 9, 9, 9, 7, 4, 3$ $\newline$ 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

1, 9, 9, 9, 7, 4, 3

\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 = $(1 + 9 + 9 + 9 + 7 + 4 + 3)/7$ $\newline$ $\mu = 42/7$ $\newline$ $\mu = 6$
Calculate Sum of Squared Differences: Data set: $1, 9, 9, 9, 7, 4, 3$
$\mu = 6$
Calculate the sum of the squared differences from the mean.
$(1 - 6)^2 + (9 - 6)^2 + (9 - 6)^2 + (9 - 6)^2 + (7 - 6)^2 + (4 - 6)^2 + (3 - 6)^2$
$= (-5)^2 + (3)^2 + (3)^2 + (3)^2 + (1)^2 + (-2)^2 + (-3)^2$
$= 25 + 9 + 9 + 9 + 1 + 4 + 9$
$= 66$
Calculate Variance: We have: $\newline$ $\Sigma(x_i - \mu)^2= 66$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{66}{7}$ $\newline$ $\sigma^2 \approx 9.4$ when rounded to the nearest tenth.