Answer to Question #271561 in Statistics and Probability for Zack

Question

In the following ordered data, the mean is 6 and the median is 5.

2,b, 3, a, 6, 9, 10, 12 Find each of the following (a) the value of a;

(b) the value of b;

Answer 1

$$mean=\dfrac{2+b+3+a+6+9+10+12}{8}=6$$

$$a+b=6$$

$$median=\dfrac{a+6}{2}=5$$

(a)

$$a=5(2)-6$$

$$a=4$$

(b)

$$4+b=6$$

$$b=2$$