In the data set below, what is the variance? 6, 4, 7, 1, 7, 5 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now, calculate the squared differences from the mean for each data point. (6 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (1 - 5)^2 + (7 - 5)^2 + (5 - 5)^2 = (1)^2 + (-1)^2 + (2)^2 + (-4)^2 + (2)^2 + (0)^2 = 1 + 1 + 4 + 16 + 4 + 0 = 26Find Variance: Next, divide the sum of squared differences by the number of data points to find the variance. N = 6 (number of data points) σ^2 = Σ(x_i - μ)^2 / N σ^2 = 26/6 σ^2 ≈ 4.3333Round to Nearest Tenth: Finally, round the variance to the nearest tenth. σ^2 ≈ 4.3

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In the data set below, what is the variance? $\newline$ $6, 4, 7, 1, 7, 5$ $\newline$ 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

6, 4, 7, 1, 7, 5

\newline

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

\newline

variance

\sigma^2

: _____

Calculate Squared Differences: Now, calculate the squared differences from the mean for each data point. $\newline$ $(6 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (1 - 5)^2 + (7 - 5)^2 + (5 - 5)^2$ $\newline$ $= (1)^2 + (-1)^2 + (2)^2 + (-4)^2 + (2)^2 + (0)^2$ $\newline$ $= 1 + 1 + 4 + 16 + 4 + 0$ $\newline$ $= 26$
Find Variance: Next, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $N = 6$ (number of data points) $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{26}{6}$ $\newline$ $\sigma^2 \approx 4.3333$
Round to Nearest Tenth: Finally, round the variance to the nearest tenth. $\sigma^2 \approx 4.3$