Question

Marks of ten students in Probability are given below 

2,3,6,8,11,a,17,20,28,b

If mean of the marks is 1.4 and median is 13. Find the values of a and b.

Answer 1

We have the sample:

2, 3, 6, 8, 11, a, 17, 20, 28, b

the mean = 14

the median = 13

The median is the value separating the higher half from the lower half, therefore

$13 = \frac{11+a}{2}\implies a = 13\cdot2-11=15$

The mean is calculated by the formula: $\mu=\frac{\sum x_i}{n}$

$\frac{2+ 3+ 6+ 8+11+ 15+ 17+20+28+b}{10}=14 \implies b = 30$

Answer:

a = 15

b = 30