Question

If the difference of mode and median of a data is 24, then the diffrence of median and mean is

Answer 1

Given,
mode-median=24
median-mean=?
A/Q,
we know,
mode=3median-2mean
mode=median+2median-2mean
mode-median=2median-2mean
24=2(median-mean)
median-mean=24/2
median-mean=12
hence,
median-mean=12.

Answer 2

Answer:

If the difference of mode and median of a data is 24, then the difference of median and mean is 12.

According to the given data;

Difference between mode and median is 24, so;

Mode - Median = 24 ⇒ (A)

We've to calculate difference of median and mode;

Median - Mode = ???

according to the basic rules of the statistics;

Mode of a given data is equal to difference of thrice of median and twice of mode, so;

Mode = 3*Median - 2*Mode ⇒ (B)

Now we know that 3*Median = Median + 2*Median, substituting the relation in equation (B) which implies;

Mode = Median + 2*Median - 2*Mode

Mode - Median = 2*Median - 2*Mode

Mode - Median = 2[ Median - Mode]

Median - Mode = (Mode - Median) / 2

Substituting the values from equation (A);

Median - Mode = 24/2 = 12

Median - Mode = 12