If the ratio of mode and median of a certain data is 6 : 5, then find

1.	If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
Answer» We know, Empirical formula: Mode = 3 Median – 2 Mean Since, ratio of mode and median of a certain data is 6:5. ⇒ \(\frac{Mode}{Median}\) = \(\frac{6}{5}\) or Mode = \(\frac{(6\, Median)}{5} \) Now, \(\frac{(6\, Median)}{5} \) = 3 Median – 2 Mean \(\frac{(6\, Median)}{5} \) – 3 Median = – 2 Mean or \(\frac{9}{10}\) (Median) = Mean or \(\frac{Mean}{Median}\) = \(\frac{9}{10}\) or 9:10.

If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.

Answer»

We know,

Empirical formula: Mode = 3 Median – 2 Mean

Since, ratio of mode and median of a certain data is 6:5.

⇒ \(\frac{Mode}{Median}\) = \(\frac{6}{5}\) or Mode = \(\frac{(6\, Median)}{5} \)

Now,

\(\frac{(6\, Median)}{5} \) = 3 Median – 2 Mean

\(\frac{(6\, Median)}{5} \) – 3 Median = – 2 Mean

or \(\frac{9}{10}\) (Median) = Mean

or \(\frac{Mean}{Median}\) = \(\frac{9}{10}\) or 9:10.