Answer to Question #165623 in Statistics and Probability for Dolly

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