In the data set below, what is the variance? 1, 5, 7, 3, 8 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Subtract and Square: Now, subtract the mean from each data point and square the result to find the squared differences. (1 - 4.8)^2 = (-3.8)^2 = 14.44 (5 - 4.8)^2 = (0.2)^2 = 0.04 (7 - 4.8)^2 = (2.2)^2 = 4.84 (3 - 4.8)^2 = (-1.8)^2 = 3.24 (8 - 4.8)^2 = (3.2)^2 = 10.24Sum Squared Differences: Sum the squared differences to find the total squared variation from the mean. Σ(x_i - μ)^2 = 14.44 + 0.04 + 4.84 + 3.24 + 10.24 Σ(x_i - μ)^2 = 32.8Calculate Variance: Divide the total squared variation by the number of data points (N) to find the variance. N = 5 (since there are 5 data points) σ^2 = Σ(x_i - μ)^2 / N σ^2 = 32.8 / 5 σ^2 = 6.56Round to Nearest Tenth: Round the variance to the nearest tenth. σ^2 ≈ 6.6

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In the data set below, what is the variance? $\newline$ $1, 5, 7, 3, 8$ $\newline$ 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

1, 5, 7, 3, 8

\newline

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

\newline

variance

\sigma^2

: _____

Subtract and Square: Now, subtract the mean from each data point and square the result to find the squared differences. $\newline$ $(1 - 4.8)^2 = (-3.8)^2 = 14.44$ $\newline$ $(5 - 4.8)^2 = (0.2)^2 = 0.04$ $\newline$ $(7 - 4.8)^2 = (2.2)^2 = 4.84$ $\newline$ $(3 - 4.8)^2 = (-1.8)^2 = 3.24$ $\newline$ $(8 - 4.8)^2 = (3.2)^2 = 10.24$
Sum Squared Differences: Sum the squared differences to find the total squared variation from the mean. $\newline$ $\Sigma(x_i - \mu)^2 = 14.44 + 0.04 + 4.84 + 3.24 + 10.24$ $\newline$ $\Sigma(x_i - \mu)^2 = 32.8$
Calculate Variance: Divide the total squared variation by the number of data points ( $N$ ) to find the variance. $\newline$ $N = 5$ (since there are $5$ data points) $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{32.8}{5}$ $\newline$ $\sigma^2 = 6.56$
Round to Nearest Tenth: Round the variance to the nearest tenth. $\sigma^2 \approx 6.6$