Question

11. The annual incomes of 5 households are $22100, 23200, 34100, 36900, 40500. Find the mean, median and standard deviation.

Answer 1

Mean:

$\mu = \frac{22100+23200+34100+36900+40500}{5} = 31360$

Variance:

$\sigma^2=\frac{1}{n}\sum_{i=1}^{n}(X_i-\mu)^2\\\\ =\frac{1}{5}\left ( \left ( 22100-\mu \right )^2+ \left ( 23200-\mu \right )^2+\left (34100-\mu \right )^2+\left ( 36900-\mu \right )^2 +\left ( 40500-\mu \right )^2\right )\\\\ =5481440$

standard deviation:

$\sigma =\sqrt{5481440} =7403.675$

median:

Median is the middlemost value of the observations if sorted in an increasing order.

Here median is : 34100