Find the Variance 30 , 32 , 47 , 57 , 66 , 79

$30$ , $32$ , $47$ , $57$ , $66$ , $79$

The mean of a set of numbers is the sum divided by the number of terms.

$\overline{x} = \frac{30 + 32 + 47 + 57 + 66 + 79}{6}$

Simplify the numerator.

Add $30$ and $32$ .

$\overline{x} = \frac{62 + 47 + 57 + 66 + 79}{6}$

Add $62$ and $47$ .

$\overline{x} = \frac{109 + 57 + 66 + 79}{6}$

Add $109$ and $57$ .

$\overline{x} = \frac{166 + 66 + 79}{6}$

Add $166$ and $66$ .

$\overline{x} = \frac{232 + 79}{6}$

Add $232$ and $79$ .

$\overline{x} = \frac{311}{6}$

Divide.

$\overline{x} = 51.8\overline{3}$

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$\overline{x} = 51.8$

Set up the formula for variance. The variance of a set of values is a measure of the spread of its values.

$s^{2} = \sum_{i = 1}^{n} \frac{{(x_{i} - x_{a v g})}^{2}}{n - 1}$

Set up the formula for variance for this set of numbers.

$s = \frac{{(30 - 51.8)}^{2} + {(32 - 51.8)}^{2} + {(47 - 51.8)}^{2} + {(57 - 51.8)}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Simplify the result.

Simplify the numerator.

Subtract $51.8$ from $30$ .

$s = \frac{{(- 21.8)}^{2} + {(32 - 51.8)}^{2} + {(47 - 51.8)}^{2} + {(57 - 51.8)}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Raise $- 21.8$ to the power of $2$ .

$s = \frac{475.24 + {(32 - 51.8)}^{2} + {(47 - 51.8)}^{2} + {(57 - 51.8)}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Subtract $51.8$ from $32$ .

$s = \frac{475.24 + {(- 19.8)}^{2} + {(47 - 51.8)}^{2} + {(57 - 51.8)}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Raise $- 19.8$ to the power of $2$ .

$s = \frac{475.24 + 392.04 + {(47 - 51.8)}^{2} + {(57 - 51.8)}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Subtract $51.8$ from $47$ .

$s = \frac{475.24 + 392.04 + {(- 4.8)}^{2} + {(57 - 51.8)}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Raise $- 4.8$ to the power of $2$ .

$s = \frac{475.24 + 392.04 + 23.04 + {(57 - 51.8)}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Subtract $51.8$ from $57$ .

$s = \frac{475.24 + 392.04 + 23.04 + {5.2}^{2} + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Raise $5.2$ to the power of $2$ .

$s = \frac{475.24 + 392.04 + 23.04 + 27.04 + {(66 - 51.8)}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Subtract $51.8$ from $66$ .

$s = \frac{475.24 + 392.04 + 23.04 + 27.04 + {14.2}^{2} + {(79 - 51.8)}^{2}}{6 - 1}$

Raise $14.2$ to the power of $2$ .

$s = \frac{475.24 + 392.04 + 23.04 + 27.04 + 201.64 + {(79 - 51.8)}^{2}}{6 - 1}$

Subtract $51.8$ from $79$ .

$s = \frac{475.24 + 392.04 + 23.04 + 27.04 + 201.64 + {27.2}^{2}}{6 - 1}$

Raise $27.2$ to the power of $2$ .

$s = \frac{475.24 + 392.04 + 23.04 + 27.04 + 201.64 + 739.84}{6 - 1}$

Add $475.24$ and $392.04$ .

$s = \frac{867.28 + 23.04 + 27.04 + 201.64 + 739.84}{6 - 1}$

Add $867.28$ and $23.04$ .

$s = \frac{890.32 + 27.04 + 201.64 + 739.84}{6 - 1}$

Add $890.32$ and $27.04$ .

$s = \frac{917.36 + 201.64 + 739.84}{6 - 1}$

Add $917.36$ and $201.64$ .

$s = \frac{1119 + 739.84}{6 - 1}$

Add $1119$ and $739.84$ .

$s = \frac{1858.84}{6 - 1}$

Simplify the expression.

Subtract $1$ from $6$ .

$s = \frac{1858.84}{5}$

Divide $1858.84$ by $5$ .

$s = 371.768$

Approximate the result.

$s^{2} \approx 371.768$

Find the Variance 30 , 32 , 47 , 57 , 66 , 79

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