Statistics Examples

$1.2$ , $3.5$ , $3.6$ , $9.2$

Step 1

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

$\overline{x} = \frac{1.2 + 3.5 + 3.6 + 9.2}{4}$

Step 2

Simplify the numerator.

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Step 2.1

Add $1.2$ and $3.5$ .

$\overline{x} = \frac{4.7 + 3.6 + 9.2}{4}$

Step 2.2

Add $4.7$ and $3.6$ .

$\overline{x} = \frac{8.3 + 9.2}{4}$

Step 2.3

Add $8.3$ and $9.2$ .

$\overline{x} = \frac{17.5}{4}$

Step 3

Divide $17.5$ by $4$ .

$\overline{x} = 4.375$

Step 4

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.

$\overline{x} = 4.38$

Step 5

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

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

Step 6

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

$s = \frac{{(1.2 - 4.38)}^{2} + {(3.5 - 4.38)}^{2} + {(3.6 - 4.38)}^{2} + {(9.2 - 4.38)}^{2}}{4 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $4.38$ from $1.2$ .

$s = \frac{{(- 3.18)}^{2} + {(3.5 - 4.38)}^{2} + {(3.6 - 4.38)}^{2} + {(9.2 - 4.38)}^{2}}{4 - 1}$

Step 7.1.2

Raise $- 3.18$ to the power of $2$ .

$s = \frac{10.1124 + {(3.5 - 4.38)}^{2} + {(3.6 - 4.38)}^{2} + {(9.2 - 4.38)}^{2}}{4 - 1}$

Step 7.1.3

Subtract $4.38$ from $3.5$ .

$s = \frac{10.1124 + {(- 0.88)}^{2} + {(3.6 - 4.38)}^{2} + {(9.2 - 4.38)}^{2}}{4 - 1}$

Step 7.1.4

Raise $- 0.88$ to the power of $2$ .

$s = \frac{10.1124 + 0.7744 + {(3.6 - 4.38)}^{2} + {(9.2 - 4.38)}^{2}}{4 - 1}$

Step 7.1.5

Subtract $4.38$ from $3.6$ .

$s = \frac{10.1124 + 0.7744 + {(- 0.78)}^{2} + {(9.2 - 4.38)}^{2}}{4 - 1}$

Step 7.1.6

Raise $- 0.78$ to the power of $2$ .

$s = \frac{10.1124 + 0.7744 + 0.6084 + {(9.2 - 4.38)}^{2}}{4 - 1}$

Step 7.1.7

Subtract $4.38$ from $9.2$ .

$s = \frac{10.1124 + 0.7744 + 0.6084 + {4.82}^{2}}{4 - 1}$

Step 7.1.8

Raise $4.82$ to the power of $2$ .

$s = \frac{10.1124 + 0.7744 + 0.6084 + 23.2324}{4 - 1}$

Step 7.1.9

Add $10.1124$ and $0.7744$ .

$s = \frac{10.8868 + 0.6084 + 23.2324}{4 - 1}$

Step 7.1.10

Add $10.8868$ and $0.6084$ .

$s = \frac{11.4952 + 23.2324}{4 - 1}$

Step 7.1.11

Add $11.4952$ and $23.2324$ .

$s = \frac{34.7276}{4 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $1$ from $4$ .

$s = \frac{34.7276}{3}$

Step 7.2.2

Divide $34.7276$ by $3$ .

$s = 11.5758\overline{6}$

Step 8

Approximate the result.

$s^{2} \approx 11.5759$

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