If the difference between the mean and median of a data is 2 x, then find the difference between the mean and mode of the data?

Question

If the difference between the mean and median of a data is 2 x, then find the difference between the mean and mode of the data? (A) 3 x (B) 6 x (C) (x/2) (D) (x/3)

Tardigrade Admin · Accepted Answer

text Mode =3 text median -2 text mean text Mode - text mean =3 text median -3 text mean text Mode - text Mean =3( text Median - text mean ) ∴ text Mode - text mean =3(2 x)=6 x ( text Since, text median - text mean =x)

Q. If the difference between the mean and median of a data is $2 x$ , then find the difference between the mean and mode of the data?

$3 x$

$6 x$

$\frac{x}{2}$

$\frac{x}{3}$

$Mode = 3 median - 2 mean$
$Mode - mean = 3 median - 3 mean$
$Mode - Mean = 3 (Median - mean)$
$∴ Mode - mean = 3 (2 x) = 6 x$
$(Since, median - mean = x)$

Q. If the difference between the mean and median of a data is 2x, then find the difference between the mean and mode of the data?

3x

6x

2x​

3x​