# What are the variance and standard deviation of {1, 1, 1, 1, 1, 7000, 1, 1, 1, 1, 1, 1, 1, 1, 1}?

Dec 17, 2016

$v a r i a n c e = 3 , 050 , 000 \left(3 s . f .\right)$
$\Sigma = 1750 \left(3 s . f .\right)$

#### Explanation:

first find the average:

average = $\frac{1 + 1 + 1 + 1 + 1 + 7000 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1}{15}$

$= \frac{7014}{15}$

$= 467.6$

find deviations for each number- this is done by subtracting the average:

$1 - 467.6 = - 466.6$

$7000 - 467.6 = 6532.4$

then square each deviation:

${\left(- 466.6\right)}^{2} = 217 , 715.56$

${6532.4}^{2} = 42 , 672 , 249.76$

the variance is the mean of these values:

variance = $\frac{\left(14 \cdot 217715.56\right) + 42672249.76}{15}$

$= 3 , 050 , 000 \left(3 s . f .\right)$

the standard deviation is the square root of the variance:

$\Sigma = \sqrt{3050000} = 1750 \left(3 s . f .\right)$