In the data set below, what is the variance? 1, 5, 5, 4, 6, 3 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum of Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. Σ(x_i - μ)^2 = (1 - 4)^2 + (5 - 4)^2 + (5 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (3 - 4)^2 = (-3)^2 + (1)^2 + (1)^2 + (0)^2 + (2)^2 + (-1)^2 = 9 + 1 + 1 + 0 + 4 + 1 = 16Find Variance: Now, divide the sum of squared differences by the number of data points to find the variance. σ^2 = Σ(x_i - μ)^2 / N σ^2 = 16 / 6 σ^2 ≈ 2.666...Round to Nearest Tenth: Finally, round the variance to the nearest tenth. σ^2 ≈ 2.7

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In the data set below, what is the variance? $\newline$ $1, 5, 5, 4, 6, 3$ $\newline$ 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, 5, 4, 6, 3

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. $\newline$ $\Sigma(x_i - \mu)^2 = (1 - 4)^2 + (5 - 4)^2 + (5 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (3 - 4)^2$ $\newline$ $= (-3)^2 + (1)^2 + (1)^2 + (0)^2 + (2)^2 + (-1)^2$ $\newline$ $= 9 + 1 + 1 + 0 + 4 + 1$ $\newline$ $= 16$
Find Variance: Now, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{16}{6}$ $\newline$ $\sigma^2 \approx 2.666...$
Round to Nearest Tenth: Finally, round the variance to the nearest tenth. $\sigma^2 \approx 2.7$