Question

5. Mount Kenya University has six different religious unions with the following number of officials: 25 30 18 27 28 22 respectively. Find the following:
a. Mean (2 marks)
b. Variance (2 marks)
c. Standard deviation (1 mark)

Answer 1

a. Mean:

$$\mu=\frac {1}{n} \sum_{i=1}^n x_i=\frac {25+30+18+27+28+22}{6}=25$$

b. Variance:

$$\sigma^2=\frac {1}{n} \sum_{i=1}^n( x_i-\mu)^2=\frac {0^2+5^2+(-7)^2+2^2+3^2+(-3)^2}{6}=16$$

c. Standard deviation:

$$\sigma=\sqrt{\frac {1}{n} \sum_{i=1}^n( x_i-\mu)^2}=\sqrt{16}=4$$