Question

a) Calculate the standard deviation and variance for the distribution below:

3, 4, 5, 5, 6, 7

b) '80, 90, 100, 110' 'and' '91, 92, 93, 94 '' value groups have been given. The standard deviation of the first group is 12.9, the second group is 1.29. Interpret the result by calculating the coefficients of variation for both value groups.

Answer 1

Standard deviation equal to square root of variance

Variance is 2

Square root of 2 =1.41

Hence, Standard deviation is 1.41

Variance equal to sum of x-x bar square divided by n-1

Sum of x-x bar square = 10

n-1= 6-5=5

Hence, variance is 10÷5=2

Variance is 2.0

Co efficient of variation= standard deviation divided by mean multiply by 100

Standard deviation of first group 12.9

Mean=total values divided by toal numbers= 80+90+100+110÷4=380÷4× =95

Coefficient of variation=standard deviation ÷mean × 100=12 .9÷95×100=13.5

Standard deviation for the second group is 1.29

Mean =Mean=total values divided by toal numbers= 91+92+93+94÷4=380÷4=92.5

Coefficient of variation=standard deviation ÷mean × 100=1.29÷92.5×100=1.39