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

Calculate Squared Differences: Now that we have the mean, we calculate the squared differences from the mean for each data point. (5 - 5)^2 + (7 - 5)^2 + (7 - 5)^2 + (7 - 5)^2 + (5 - 5)^2 + (3 - 5)^2 + (1 - 5)^2 = 0^2 + 2^2 + 2^2 + 2^2 + 0^2 + (-2)^2 + (-4)^2 = 0 + 4 + 4 + 4 + 0 + 4 + 16 = 32Find Variance: Finally, we 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 = 32 / 7 σ^2 ≈ 4.57142857143 Rounded to the nearest tenth: σ^2 ≈ 4.6

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In the data set below, what is the variance? $\newline$ $5, 7, 7, 7, 5, 3, 1$ $\newline$ 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

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

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now that we have the mean, we calculate the squared differences from the mean for each data point. $\newline$ $(5 - 5)^2 + (7 - 5)^2 + (7 - 5)^2 + (7 - 5)^2 + (5 - 5)^2 + (3 - 5)^2 + (1 - 5)^2$ $\newline$ $= 0^2 + 2^2 + 2^2 + 2^2 + 0^2 + (-2)^2 + (-4)^2$ $\newline$ $= 0 + 4 + 4 + 4 + 0 + 4 + 16$ $\newline$ $= 32$
Find Variance: Finally, we 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 $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{32}{7}$ $\newline$ $\sigma^2 \approx 4.57142857143$ $\newline$ Rounded to the nearest tenth: $\sigma^2 \approx 4.6$