Basic Math Examples

$7.82$ , $7.83$ , $7.7$ , $7.81$ , $7.75$

Step 1

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

$\overline{x} = \frac{7.82 + 7.83 + 7.7 + 7.81 + 7.75}{5}$

Step 2

Simplify the numerator.

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Step 2.1

Add $7.82$ and $7.83$ .

$\overline{x} = \frac{15.65 + 7.7 + 7.81 + 7.75}{5}$

Step 2.2

Add $15.65$ and $7.7$ .

$\overline{x} = \frac{23.35 + 7.81 + 7.75}{5}$

Step 2.3

Add $23.35$ and $7.81$ .

$\overline{x} = \frac{31.16 + 7.75}{5}$

Step 2.4

Add $31.16$ and $7.75$ .

$\overline{x} = \frac{38.91}{5}$

Step 3

Divide $38.91$ by $5$ .

$\overline{x} = 7.782$

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.

$\overline{x} = 7.782$

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.

$s = \frac{{(7.82 - 7.782)}^{2} + {(7.83 - 7.782)}^{2} + {(7.7 - 7.782)}^{2} + {(7.81 - 7.782)}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7

Simplify the result.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Subtract $7.782$ from $7.82$ .

$s = \frac{{0.038}^{2} + {(7.83 - 7.782)}^{2} + {(7.7 - 7.782)}^{2} + {(7.81 - 7.782)}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.2

Raise $0.038$ to the power of $2$ .

$s = \frac{0.001444 + {(7.83 - 7.782)}^{2} + {(7.7 - 7.782)}^{2} + {(7.81 - 7.782)}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.3

Subtract $7.782$ from $7.83$ .

$s = \frac{0.001444 + {0.048}^{2} + {(7.7 - 7.782)}^{2} + {(7.81 - 7.782)}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.4

Raise $0.048$ to the power of $2$ .

$s = \frac{0.001444 + 0.002304 + {(7.7 - 7.782)}^{2} + {(7.81 - 7.782)}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.5

Subtract $7.782$ from $7.7$ .

$s = \frac{0.001444 + 0.002304 + {(- 0.082)}^{2} + {(7.81 - 7.782)}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.6

Raise $- 0.082$ to the power of $2$ .

$s = \frac{0.001444 + 0.002304 + 0.006724 + {(7.81 - 7.782)}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.7

Subtract $7.782$ from $7.81$ .

$s = \frac{0.001444 + 0.002304 + 0.006724 + {0.028}^{2} + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.8

Raise $0.028$ to the power of $2$ .

$s = \frac{0.001444 + 0.002304 + 0.006724 + 0.000784 + {(7.75 - 7.782)}^{2}}{5 - 1}$

Step 7.1.9

Subtract $7.782$ from $7.75$ .

$s = \frac{0.001444 + 0.002304 + 0.006724 + 0.000784 + {(- 0.032)}^{2}}{5 - 1}$

Step 7.1.10

Raise $- 0.032$ to the power of $2$ .

$s = \frac{0.001444 + 0.002304 + 0.006724 + 0.000784 + 0.001024}{5 - 1}$

Step 7.1.11

Add $0.001444$ and $0.002304$ .

$s = \frac{0.003748 + 0.006724 + 0.000784 + 0.001024}{5 - 1}$

Step 7.1.12

Add $0.003748$ and $0.006724$ .

$s = \frac{0.010472 + 0.000784 + 0.001024}{5 - 1}$

Step 7.1.13

Add $0.010472$ and $0.000784$ .

$s = \frac{0.011256 + 0.001024}{5 - 1}$

Step 7.1.14

Add $0.011256$ and $0.001024$ .

$s = \frac{0.01228}{5 - 1}$

Step 7.2

Simplify the expression.

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Step 7.2.1

Subtract $1$ from $5$ .

$s = \frac{0.01228}{4}$

Step 7.2.2

Divide $0.01228$ by $4$ .

$s = 0.00307$

Step 8

Approximate the result.

$s^{2} \approx 0.0031$