In the data set below, what is the variance? 3, 3, 7, 2, 1, 7, 5 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Mean: Calculate the mean of the data set. question_prompt: What is the variance of the given data set? To find the variance, we first need to calculate the mean (average) of the data set. Mean μ = (3 + 3 + 7 + 2 + 1 + 7 + 5)/7 μ = 28/7 μ = 4Calculate Squared Differences: Calculate the squared differences from the mean for each data point. Now that we have the mean, we calculate the squared differences from the mean for each data point. (3 - 4)^2 + (3 - 4)^2 + (7 - 4)^2 + (2 - 4)^2 + (1 - 4)^2 + (7 - 4)^2 + (5 - 4)^2 = (-1)^2 + (-1)^2 + (3)^2 + (-2)^2 + (-3)^2 + (3)^2 + (1)^2 = 1 + 1 + 9 + 4 + 9 + 9 + 1 = 34Find Variance: Divide the sum of squared differences by the number of data points to find the variance. We have the sum of the squared differences, which is 34. To find the variance, we divide this sum by the number of data points, N, which is 7. σ^2 = Σ(x_i - μ)^2 / N σ^2 = 34 / 7 σ^2 ≈ 4.857 Since we need to round to the nearest tenth, the variance is approximately 4.9.

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In the data set below, what is the variance? $\newline$ $3, 3, 7, 2, 1, 7, 5$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

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Algebra 1

Variance and standard deviation

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Q. In the data set below, what is the variance?

\newline

3, 3, 7, 2, 1, 7, 5

\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. $\newline$ question_prompt: What is the variance of the given data set? $\newline$ To find the variance, we first need to calculate the mean (average) of the data set. $\newline$ Mean $\mu = \frac{3 + 3 + 7 + 2 + 1 + 7 + 5}{7}$ $\newline$ $\mu = \frac{28}{7}$ $\newline$ $\mu = 4$
Calculate Squared Differences: Calculate the squared differences from the mean for each data point. $\newline$ Now that we have the mean, we calculate the squared differences from the mean for each data point. $\newline$ $(3 - 4)^2 + (3 - 4)^2 + (7 - 4)^2 + (2 - 4)^2 + (1 - 4)^2 + (7 - 4)^2 + (5 - 4)^2$ $\newline$ $= (-1)^2 + (-1)^2 + (3)^2 + (-2)^2 + (-3)^2 + (3)^2 + (1)^2$ $\newline$ $= 1 + 1 + 9 + 4 + 9 + 9 + 1$ $\newline$ $= 34$
Find Variance: Divide the sum of squared differences by the number of data points to find the variance. $\newline$ We have the sum of the squared differences, which is $34$ . To find the variance, we divide this sum by the number of data points, $N$ , which is $7$ . $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{34}{7}$ $\newline$ $\sigma^2 \approx 4.857$ $\newline$ Since we need to round to the nearest tenth, the variance is approximately $4.9$ .