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

Question

If X, M, Z are denoting mean, median and mode of a data and X: M=9: 8, then find the ratio M: Z. (A) 8: 9 (B) 4: 3 (C) 7: 6 (D) 5: 4

Tardigrade Admin · Accepted Answer

text Mode =3 × text Median -2 × text Mean Z=3 M-2 X text Given, X: M=9: 8 ⇒ (X/M)=(9/8) X=(9 M/8) ∴ Z=3 M-2 × (9 M/8)=3 M-(9 M/4) Z=(3 M/4) ∴ (M/Z)=(4/3) ⇒ M: Z=4: 3 .

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

$8 : 9$

$4 : 3$

$7 : 6$

$5 : 4$

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

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.

8:9

4:3

7:6

5:4