In the data set below, what is the variance? 6, 6, 4, 7, 3, 2, 7 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 - mean)^2 = (6 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (3 - 5)^2 + (2 - 5)^2 + (7 - 5)^2 Σ(x_i - mean)^2 = (1)^2 + (1)^2 + (-1)^2 + (2)^2 + (-2)^2 + (-3)^2 + (2)^2 Σ(x_i - mean)^2 = 1 + 1 + 1 + 4 + 4 + 9 + 4 Σ(x_i - mean)^2 = 24Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. Variance (σ^2) = Σ(x_i - mean)^2 / N Variance (σ^2) = 24 / 7 Variance (σ^2) ≈ 3.4 (rounded to the nearest tenth)

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In the data set below, what is the variance? $\newline$ $6, 6, 4, 7, 3, 2, 7$ $\newline$ 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

6, 6, 4, 7, 3, 2, 7

\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. $\newline$ $\Sigma(x_i - \text{mean})^2 = (6 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (3 - 5)^2 + (2 - 5)^2 + (7 - 5)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = (1)^2 + (1)^2 + (-1)^2 + (2)^2 + (-2)^2 + (-3)^2 + (2)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 1 + 1 + 1 + 4 + 4 + 9 + 4$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 24$
Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. $\newline$ Variance $\sigma^2$ = $\frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{24}{7}$ $\newline$ Variance $\sigma^2$ $\approx 3.4$ (rounded to the nearest tenth)