question_answer

If empirical relationship between mean, median and mode is expressed as mean \[=k\](3 median\[\]mode), then find the value of\[k\].

Answer:

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 \[=2\text{ }k\]mean

\[2k\]mean\[\]mean \[=0\]

\[\text{mean}\,[2k-1]=0\]

\[2k-1=0\]

\[2k=0+1\]

\[k=1/2\]