This document provides information about the relationship between the mean, median, and mode of a moderately skewed distribution. It states that for a moderately skewed distribution, the difference between the mean and mode is equal to three times the difference between the mean and median. This relationship is represented by the formula: Mean – Mode = 3(Mean – Median). The document provides three examples of using this formula to calculate the missing statistical measure when given the other two. It concludes by providing three practice problems for the reader to solve on their own.

1. NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS
https://www.slideshare.net/NadeemUddin17
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2. i) Median lies between mean and mode.
ii) Median closer to mean than mode.
iii) In the case of a moderately skewed distribution, the difference
between mean and mode is equal to three times the difference
between the mean and median.
In moderately skewed distribution, the following approximate
relation holds good.
Mean – Mode = 3 (Mean – Median)
OR
Mode = 3 Median – 2 Mean
This empirical relation does not hold in case of a J – shaped or
an extremely skewed distribution.

3. Example -1
For a certain frequency distribution, the mean was 40.5 and median 36.
Find the mode using the formula connecting the three.
Solution:
Given that:
Mean = 40.5, Median = 36, Mode = ?
We know that:
Mean – Mode = 3 (Mean – Median)
40.5 – Mode = 3 (40.5 – 36)
40.5 – Mode = 3  4.5
40.5 – Mode = 13.5
Mode = 40.5 – 13.5
Mode = 27

4. Example -2
For a certain frequency distribution, the mode was 27 and median 36.
Find the mean using the formula connecting the three.
Solution:
Given that:
Median = 36, Mode = 27 , Mean = ?
We know that:
Mode = 3Median - 2Mean
27 = 3 (36) - 2Mean
27 = 108 - 2Mean
27 - 108 = - 2Mean
- 81 = - 2Mean
Mean =
81
2
Mean = 40.5

5. Example -3
For a certain frequency distribution, the mode was 27 and mean 40.5.
Find the median using the formula connecting the three.
Solution:
Given that:
Mode = 27 , Mean = 40.5, Median = ?
We know that:
Mode = 3Median - 2Mean
27 = 3Median – 2(40.5)
27 = 3Median – 81
27 + 81 = 3Median
108 = 3Median
Median =
108
3
Median = 36

6. DO YOURSELF
i) In a moderately asymmetrical series, the value of arithmetic
mean and median is 20 and 18.67 respectively. Find out the
value of Mode. (Answer = 16.01)
ii) In a moderately skewed distribution, mode = 10
and median = 30, then find the mean. (Answer = 40)
iii) In a moderately asymmetrical distribution the mode and mean
are 32.1 and 35.4 respectively.
Calculate the median. (Answer = 34.3)