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How is the mode calculated on the basis of arithmetic mean and median? |
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Answer» The mutual relationship between these three averages depends on whether the series is symmetrical or asymmetrical. Symmetrical Series : In these series the value of arithmetic mean, median and mode are equal. Asymmetric Series : In these series the values of these three average are different and generally \((\overline X - Z)\) is equal to 3 \((\overline X - M).\) In this situation, if the value of the two means is known, then the probable value of the third can be determined by the following formula- \((\overline X - Z) = 3 (\overline X - M)\) Z= 3 M-2 \(\overline X\) Example : If the arithmetic mean of the distribution is 20.2 and median is 31.6 then what will be the most likely value of the mode? \((\overline X - Z) = 3 (\overline X - M)\) Z = 3M – 2 \(\overline X\) Z= (3 × 31.6 ) – (2 × 20.2) = 94.8 – 40.4 = 54.4 |
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