1. 1

2. 2
Empirical Relation Between Mean , Median and Mode
If
Mean = Mode = Median
Then the distribution of the data is called symmetrical distribution.
Mean = Median = Mode

3. 3
Skewed distribution
Positively Skewed Negatively Skewed
Mode Median Mean Mean Median Mode

4. 4
Empirical Relation Between Mean , Median and Mode
If these values differ, then the frequency distribution is said to be
Skewed or asymmetrical
Skewed may be
1. Positively Skewed Distribution
2. Negatively Skewed Distribution
Positively Skewed Distribution
By positively skewed distribution we mean that the tail of the
distribution extends to the right.
For moderately positively skewed distribution the following
empirical relation holds
ModeMedianMean 

5. 5
Empirical Relation Between Mean , Median and Mode
For moderately skewed distribution median divides the distance
Between mean and mode in the ratio 1: 2.
Negatively Skewed Distribution
By negatively skewed distribution we mean that the tail of the
distribution extends to the left.
For moderately negatively skewed distribution the following
empirical relation holds
ModeMedianMean 
2
1



ModeMedian
MedianMean
Mode = 3(median) - 2(mean)or

6. Mode
Median
Mean
X
f
This diagrammatic picture is equivalent to the
following algebraic expression:
Median - Mode 2 (Mean - Median) ------ (1)~

7. The above-mentioned point can also be expressed in
the following way:
Mean – Mode 3 (Mean – Median) ---- (2)~
Equation (1) as well as equation (2) yields the
approximate relation given below:
EMPIRICAL RELATION
BETWEEN THE MEAN,
MEDIAN AND THE MODE
Mode 3 Median – 2 Mean
~