Question

The arithmetic mean and mode of a data are 24 and 12 respectively, then find the median of the data.

Answer 1

Given that the arithmetic mean and mode of a data are 24 and 12 respectively. That is,

MEAN = 24 

MODE = 12

We have to find median

We know that

MODE = 3 × MEDIAN - 2 × MEAN

⇒ 12 = 3 × MEDIAN - 2 ×  24 

⇒ 3 × MEDIAN = 12 +(2 × 24) 

⇒ 3 × MEDIAN = 12+ 48 

⇒ 3 × MEDIAN = 60

⇒ MEDIAN = `60/3`

⇒ MEDIAN = 20