Q.Explain the empirical relationship among mean, median and mode. Under what condition are all three exactly equal?

The three averages coincide only for a perfectly symmetrical distribution; for a moderately skewed one, a well-known empirical formula connects them. …

For a perfectly symmetrical distribution — one whose two halves are exact mirror images of each other about the centre — the mean, median and mode all take the same value:

Most real economic data, however, is only moderately asymmetrical (skewed), since a few unusually large or small values pull the mean away from the middle of the data while leaving the median and mode comparatively undisturbed. For such moderately skewed distributions, Karl Pearson's empirical relationship connects the three:

$Mode = 3\,Median - 2\,Mean$ …

Stating the empirical relationship as an exact law true for ANY distribution, rather than an approximation valid specifically for MODERATELY skewed data — for a highly (seve …