Question

If empiricial relationship between mean, median and mode is expressed as mean = k(3 median - mode), then find the value of k.

Answer 1

Given, mean = k(3 median - mode)
As we know, mode = 3 median - 2 mean
$\therefore$ mean = k [3 median - (3 median -2 mean)]
mean = k [3 median - 3 median + 2 mean]
mean = 2 k mean
2k mean - mean = 0
mean [2k-1] = 0
$\therefore$ 2k-1 = 0
2k = 0 + 1
$k=\frac{1}{2}$