If the ratio of the mode to the median is 7 : 9 for a dataset. Find the ratio of mode to mean

If the ratio of the mode to the median is 7 : 9 for a dataset. Find the ratio of mode to mean.

(a) 14:23

(b) 7:10

(c) 11:23

(d) 7:11

Sol:

The empirical relationship between mean mode and median is

Mode = 3 Median – 2 Mean.

Let the mode value be 7x, and the median be 9x, then

7x = 3(9x) – 2 Mean

⇒ 2Mean = 27x – 7x

⇒ Mean = 10x

∴ Mode : Mean = 7x/10x

= 7:10