Question

The following data represents the age (in years) of a sample of 25 members of parliament in a South Asia. 20 40 56 23 42 61 27 42 64 28 43 31 44 33 44 35 47 35 48 36 49 38 52 39 53 a) Compute the coefficient of variation. b) Compute the range approximation to the standard deviation of the data.

Answer 1

$n = 25$

Sample Mean  $Sample Mean \bar{X} = \frac{\sum X_{i}}{n} = \frac{1030}{25} = 41.2$

Point Estimate of the population Mean= 41.2

Sample variance $s^2 = \frac{1}{n -1} (\sum Xi^2-\frac{1}{n}(\sum Xi)^2$

$= [\frac{1}{(25 - 1)}][45432 - (\frac{1030^{2}}{25}) ] = 124.8333$

Point Estimate of the Population Variance = 124.8333

sample standard deviation s$=\sqrt{ variance }=\sqrt{ 124.8333}=11.1729$

Point Estimate of the Population Standard deviation = 11.1729

The coefficient of variation$= (\frac{sample\space standard\space deviation }{ sample \space mean})\times100$

$= (\frac{11.1729}{41.2})\times100 = 27.12\%$

The coefficient of variation is 27.12%

b)

Standard deviation = Range / 4

Range = standard deviation$\times$ 4

$= 11.1729 \times4 = 44.6916$

The range approximation to the standard deviation of the data is 44.6916