Question

The median of a set of eight numbers is 4.5. Given that seven of the numbers are 7, 2,13, 4, 8, 2 and 1, find the eight number and write down the mode of eight numbers. 

(a) 4 

(b) 7 

(c) 2 

(d) 1

Answer 1

(c) 2

Let the eighth number be x. Then the numbers arranged in ascending order: 1, 2, 2, 4, 7, 8, 13, x 

Since these are 8 in number,

Median value = \(\frac{(\frac82)th\,value+(\frac82+1)th\,value}{2}\)

= \(\frac{\text{4th value + 5th value}}{2}\)

= \(\frac{4+7}{2}=\frac{11}2\) = 5.5

∴ Mode = 2