Karl Pearson has expressed this relationship as follows

**Empirical
Relationship among mean, median and mode**

A
frequency distribution in which the values of arithmetic mean, median and mode
coincide is known of symmetrical distribution, when the values of mean, median
and mode are not equal the distribution is known as asymmetrical or skewed. In
moderately skewed asymmetrical distributions a very important relationship
exists among arithmetic mean, median and mode.

Karl
Pearson has expressed this relationship as follows

**Mode = 3 Median – 2 Arithmetic Mean**

In
a moderately asymmetrical frequency distribution, the values of median and
arithmetic mean are 72 and 78 respectively; estimate the value of the mode.

The
value of the mode is estimated by applying the following formula:

Mode
= 3 Median – 2 Mean = 3 (72) – 2 (78)

216
- 156 = 60 Mode = 60

In
a moderately asymmetrical frequency distribution, the values of mean and mode
are 52.3 and 60.3 respectively, Find the median value.

The
value of the median is estimated by applying the formula:

Mode
= 3 Median – 2 Mean

60.3 = 3 Median – 2 × 52.3

3 Median = 60.3 + 2 × 52.3

60.3 + 104.6 = 164.9

Median = 164.9/3 = 54.966 = 54.97

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11th Statistics : Chapter 5 : Measures of Central Tendency : Empirical Relationship among mean, median and mode |

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