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  4. If X, M, Z are denoting mean, median and mode of a data and X: M=9: 8, then find the ratio M: Z.

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Q. If $X, M, Z$ are denoting mean, median and mode of a data and $X: M=9: 8$, then find the ratio $M: Z$.

Statistics

Solution:

$\text { Mode }=3 \times \text { Median }-2 \times \text { Mean } $
$ Z=3 M-2 X $
$ \text { Given, } X: M=9: 8 $
$ \Rightarrow \frac{X}{M}=\frac{9}{8} $
$ X=\frac{9 M}{8}$
$ \therefore Z=3 M-2 \times \frac{9 M}{8}=3 M-\frac{9 M}{4} $
$ Z=\frac{3 M}{4} \therefore \frac{M}{Z}=\frac{4}{3} $
$ \Rightarrow M: Z=4: 3 .$