Question

If the empirical representation between mean , mode and median is mode = k(3median - 2mean) then find the value of k .

Answer 1

Dear student
$$\begin{gathered} \mathrm{Given}:\mathrm{Mode}=\mathrm{k}\left(3\mathrm{median}-2\mathrm{mean}\right)..\left(1\right) \\ \mathrm{We}\mathrm{know}\mathrm{that} \\ 3\mathrm{median}=\mathrm{mode}+2\mathrm{mean} \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}3\mathrm{median}\mathrm{in}\left(1\right),\mathrm{we}\mathrm{get} \\ \mathrm{Mode}=\mathrm{k}\left[\mathrm{mode}+2\mathrm{mean}-2\mathrm{mean}\right] \\ \Rightarrow \mathrm{mode}=\mathrm{k}\left[\mathrm{mode}\right] \\ \Rightarrow \mathrm{k}=1 \end{gathered}$$
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