In the data set below, what is the variance? 6, 7, 5, 8, 3, 7, 6 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. Σ(x_i - mean)^2 = (6 - 6)^2 + (7 - 6)^2 + (5 - 6)^2 + (8 - 6)^2 + (3 - 6)^2 + (7 - 6)^2 + (6 - 6)^2 Σ(x_i - mean)^2 = 0 + 1 + 1 + 4 + 9 + 1 + 0 Σ(x_i - mean)^2 = 16Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. variance = Σ(x_i - mean)^2 / N variance = 16 / 7 variance ≈ 2.3 when rounded to the nearest tenth.

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In the data set below, what is the variance? $\newline$ $6, 7, 5, 8, 3, 7, 6$ $\newline$ 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, 7, 5, 8, 3, 7, 6

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \text{mean})^2 = (6 - 6)^2 + (7 - 6)^2 + (5 - 6)^2 + (8 - 6)^2 + (3 - 6)^2 + (7 - 6)^2 + (6 - 6)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 0 + 1 + 1 + 4 + 9 + 1 + 0$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 16$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\text{variance} = \frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ $\text{variance} = \frac{16}{7}$ $\newline$ $\text{variance} \approx 2.3$ when rounded to the nearest tenth.