In the data set below, what is the variance? 5, 2, 1, 1, 9, 3, 7 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Variance: Now, let's do the variance part. We need to sum up each (number - mean)^2. So, (5 - 4)^2 + (2 - 4)^2 + (1 - 4)^2 + (1 - 4)^2 + (9 - 4)^2 + (3 - 4)^2 + (7 - 4)^2 That's (1)^2 + (-2)^2 + (-3)^2 + (-3)^2 + (5)^2 + (-1)^2 + (3)^2 Which is 1 + 4 + 9 + 9 + 25 + 1 + 9 Sum = 58Sum of Squares: Finally, divide that sum by the number of data points to get the variance. Variance = 58 / 7 Variance = 8.2857... Round it to the nearest tenth and we get 8.3

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In the data set below, what is the variance? $\newline$ $5, 2, 1, 1, 9, 3, 7$ $\newline$ 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

5, 2, 1, 1, 9, 3, 7

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Variance: Now, let's do the variance part. $\newline$ We need to sum up each $(\text{number} - \text{mean})^2$ . $\newline$ So, $(5 - 4)^2 + (2 - 4)^2 + (1 - 4)^2 + (1 - 4)^2 + (9 - 4)^2 + (3 - 4)^2 + (7 - 4)^2$ $\newline$ That's $(1)^2 + (-2)^2 + (-3)^2 + (-3)^2 + (5)^2 + (-1)^2 + (3)^2$ $\newline$ Which is $1 + 4 + 9 + 9 + 25 + 1 + 9$ $\newline$ Sum = $58$
Sum of Squares: Finally, divide that sum by the number of data points to get the variance. $\newline$ Variance = $\frac{58}{7}$ $\newline$ Variance = $8.2857\ldots$ $\newline$ Round it to the nearest tenth and we get $8.3$