Find the mean and variance for the data $6,7,10,12,13,4,8,12$
Find the mean and variance for the data $6,7,10,12,13,4,8,12$
$6,7,10,12,13,4,8,12$
Mean, $\bar x = \frac{{\sum\limits_{i = 1}^8 {{x_i}} }}{n}$
$=\frac{6+7+10+12+13+4+8+12}{8}=\frac{72}{8}=9$
The following table is obtained
| ${x_i}$ | $\left( {{x_i} - \bar x} \right)$ | ${\left( {{x_i} - \bar x} \right)^2}$ |
| $6$ | $-3$ | $9$ |
| $7$ | $-2$ | $4$ |
| $10$ | $-1$ | $1$ |
| $12$ | $3$ | $9$ |
| $13$ | $4$ | $16$ |
| $4$ | $-5$ | $25$ |
| $8$ | $-1$ | $1$ |
| $12$ | $3$ | $9$ |
| $74$ |
Variance $\left( {{\sigma ^2}} \right) = \frac{1}{n}\sum\limits_{i = 1}^8 {{{\left( {{x_i} - \bar x} \right)}^2} = \frac{1}{8} \times 74} = 9.25$
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