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4.6 Empirical Relation Between Mean, Median And Mode

A distribution in which the values of mean, median and mode coincide (i.e. mean = median = mode) is known as a symmetrical distribution. Conversely, when values of mean, median and mode are not equal the distribution is known as asymmetrical or skewed distribution. In moderately skewed or asymmetrical distribution a very important relationship exists among these three measures of central tendency. In such distributions the distance between the mean and median is about one-third of the distance between the mean and mode, as will be clear from the diagrams 1 and 2. Karl Pearson expressed this relationship as:

Mode = mean - 3 [mean - median]

Mode = 3 median - 2 mean

Knowing any two values, the third can be computed.

This is about the special kind of distribution which you never see on GMAT.

Again if set is for example: {1,1,1,5,7} Mean=5 Median=1 Mode=1

Put these values in the formula in red. You'll see the equation won't hold true.

I wouldn't advise to study this source in GMAT preparation. _________________

Re: Statistics - Rules and Tips [#permalink]
04 Jan 2012, 04:54

Could somebody elaborate on point 4?

I don't see how knowing the difference between the value and the total numbers of terms gives you the SD, or is it supposed to be the difference between the values and the mean?

Re: STANDARD DEVIATION : Calculation of Standard Deviation (SD) [#permalink]
16 Jul 2014, 00:42

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