In the data set below, what is the variance? 4, 3, 6, 7, 3, 3, 2 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now, we will calculate the squared differences from the mean for each data point. (4 - 4)^2 + (3 - 4)^2 + (6 - 4)^2 + (7 - 4)^2 + (3 - 4)^2 + (3 - 4)^2 + (2 - 4)^2 = 0^2 + (-1)^2 + 2^2 + 3^2 + (-1)^2 + (-1)^2 + (-2)^2 = 0 + 1 + 4 + 9 + 1 + 1 + 4 = 20Calculate Variance: Finally, we will calculate the variance by dividing the sum of squared differences by the number of data points (N). σ^2 = Σ(x_i - μ)^2 / N σ^2 = 20 / 7 σ^2 ≈ 2.857 Since we need to round to the nearest tenth, the variance is approximately 2.9.

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

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

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now, we will calculate the squared differences from the mean for each data point. $\newline$ $(4 - 4)^2 + (3 - 4)^2 + (6 - 4)^2 + (7 - 4)^2 + (3 - 4)^2 + (3 - 4)^2 + (2 - 4)^2$ $\newline$ = $0^2 + (-1)^2 + 2^2 + 3^2 + (-1)^2 + (-1)^2 + (-2)^2$ $\newline$ = $0 + 1 + 4 + 9 + 1 + 1 + 4$ $\newline$ = $20$
Calculate Variance: Finally, we will calculate the variance by dividing the sum of squared differences by the number of data points $N$ . $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\sigma^2 = \frac{20}{7}$ $\sigma^2 \approx 2.857$ Since we need to round to the nearest tenth, the variance is approximately $2.9$ .