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
