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6. An empirical relationship between mean, median and mode

In the previous topics, we have learnt how to find the mean, median and mode. From those, we can see an approximate relationship between these

$3$ measures of central tendency. And, the relationship between them is given by:

Mode

$\approx 3$ Median

$- 2$ Mean

Example:

Find the mode, if in distribution the median and mean are

$30$ and

$12$ respectively.

Solution:

Given that Median

$= 30$ and Mean

$= 12$

To find the mode.

We know the mode can be determined using the empirical formula:

Mode

$\approx 3$ Median

$- 2$ Mean

Substituting the known values in the above formula, we have:

Mode

$\approx 3(30) - 2(12)$

Mode

$\approx 90 - 24$

Mode

$\approx 66$

Therefore, the mode is

$66$ (approx.)

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