In the data set below, what is the variance? 5, 5, 5, 8, 5, 5 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum Squared Differences: Now, let's calculate the sum of the squared differences from the mean. Σ(x_i - μ)^2 = (5 - 5.5)^2 + (5 - 5.5)^2 + (5 - 5.5)^2 + (8 - 5.5)^2 + (5 - 5.5)^2 + (5 - 5.5)^2 Σ(x_i - μ)^2 = (-0.5)^2 + (-0.5)^2 + (-0.5)^2 + (2.5)^2 + (-0.5)^2 + (-0.5)^2 Σ(x_i - μ)^2 = 0.25 + 0.25 + 0.25 + 6.25 + 0.25 + 0.25 Σ(x_i - μ)^2 = 7.5Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. σ^2 = Σ(x_i - μ)^2 / N σ^2 = 7.5 / 6 σ^2 = 1.25 Since we need to round to the nearest tenth, σ^2 ≈ 1.3

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In the data set below, what is the variance? $\newline$ $5, 5, 5, 8, 5, 5$ $\newline$ 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

5, 5, 5, 8, 5, 5

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \mu)^2 = (5 - 5.5)^2 + (5 - 5.5)^2 + (5 - 5.5)^2 + (8 - 5.5)^2 + (5 - 5.5)^2 + (5 - 5.5)^2$ $\newline$ $\Sigma(x_i - \mu)^2 = (-0.5)^2 + (-0.5)^2 + (-0.5)^2 + (2.5)^2 + (-0.5)^2 + (-0.5)^2$ $\newline$ $\Sigma(x_i - \mu)^2 = 0.25 + 0.25 + 0.25 + 6.25 + 0.25 + 0.25$ $\newline$ $\Sigma(x_i - \mu)^2 = 7.5$
Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{7.5}{6}$ $\newline$ $\sigma^2 = 1.25$ $\newline$ Since we need to round to the nearest tenth, $\sigma^2 \approx 1.3$