In the data set below, what is the variance? 6, 1, 4, 5, 1, 2, 2 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum Squared Differences: Now, we will calculate the sum of the squared differences from the mean for each data point. Σ(x_i - μ)^2 = (6 - 3)^2 + (1 - 3)^2 + (4 - 3)^2 + (5 - 3)^2 + (1 - 3)^2 + (2 - 3)^2 + (2 - 3)^2 = (3)^2 + (-2)^2 + (1)^2 + (2)^2 + (-2)^2 + (-1)^2 + (-1)^2 = 9 + 4 + 1 + 4 + 4 + 1 + 1 = 24Divide by Number of Data Points: Finally, we will divide the sum of squared differences by the number of data points to find the variance. Number of data points N = 7 Variance σ^2 = Σ(x_i - μ)^2 / N σ^2 = 24 / 7 σ^2 ≈ 3.42857142857 Rounded to the nearest tenth, σ^2 ≈ 3.4

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? $\newline$ $6, 1, 4, 5, 1, 2, 2$ $\newline$ 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, 1, 4, 5, 1, 2, 2

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum Squared Differences: Now, we will calculate the sum of the squared differences from the mean for each data point. $\newline$ $\Sigma(x_i - \mu)^2 = (6 - 3)^2 + (1 - 3)^2 + (4 - 3)^2 + (5 - 3)^2 + (1 - 3)^2 + (2 - 3)^2 + (2 - 3)^2$ $\newline$ $= (3)^2 + (-2)^2 + (1)^2 + (2)^2 + (-2)^2 + (-1)^2 + (-1)^2$ $\newline$ $= 9 + 4 + 1 + 4 + 4 + 1 + 1$ $\newline$ $= 24$
Divide by Number of Data Points: Finally, we will divide the sum of squared differences by the number of data points to find the variance. $\newline$ Number of data points $N = 7$ $\newline$ Variance $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{24}{7}$ $\newline$ $\sigma^2 \approx 3.42857142857$ $\newline$ Rounded to the nearest tenth, $\sigma^2 \approx 3.4$