EMPRICAL RELATIONSHIP BETWEEN MEAN MEDIAN AND MODE

There is an approximate relation that holds among the three measures of central tendency mean, median and mode, when the frequencies are nearly symmetrically distributed.

Mode  ≈  3 Median – 2 Mean

Example 1 : 

In a distribution, the mean and median are 15 and 17 respectively. Calculate the mode. 

Solution : 

Given, Mean = 15 and Median = 17.

Empirical Relationship :

Mode  ≈  3Median – 2Mean

Substitute. 

Mode  ≈  3(15) – 2(17)

Mode  ≈  45 - 34

Mode  ≈  11

Example 2 : 

In a distribution, the mean and mode are 66 and 60 respectively. Calculate the median.

Solution : 

Given, Mean = 66 and Mode = 60.

Empirical Relationship :

Mode  ≈  3Median – 2Mean

Substitute. 

60  ≈  3Median – 2(66)

60  ≈  3Median - 132

Add 132 to each side. 

192  ≈  3Median

Divide each side by 3. 

64  ≈  Median

Example 3 : 

For a moderately skewed distribution of marks in statistics for a group of 200 students, the mean mark and medina mark were found to be 55.60 and 52.40. What is the modal mark? 

Solution : 

Given, Mean = 55.60 and Median = 52.40.

Empirical Relationship :

Mode  ≈  3Median – 2Mean

Substitute. 

Mode  ≈  3(52.40) – 2(55.60)

Mode  ≈  157.20 - 111.20

Mode  ≈  46

So, the modal mark is 46.

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