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1.5.5. Differences and Relationship among Basic Measures of Central Tendency
There is a huge difference between basic measures of central tendency, i.e., mean, median and mode. These shall
be equal in case of normal distribution. They will be almost equal in case of slightly positive or negatively skewed
distribution.
But, there is also a relationship between mean, median, and mode. We term this relationship as the empirical
relationship.
Relationship Between Mean, Median, and Mode
We will recognise the empirical relationship between mean, median, and mode by using a frequency distribution
graph. We can divide the relationship into four different cases:
1. In the case of a moderately skewed distribution, i.e., in general, the difference between mean and mode is equal
to three times the difference between the mean and median.
Thus, the empirical relationship as Mean – Mode = 3 (Mean – Median)
2. In the case of a frequency distribution that has a symmetrical frequency curve, the empirical relation states that
mean = median = mode.
Frequency Mean = Median = Mode
x Variable
3. In the case of a positively skewed frequency distribution curve, mean > median > mode
Mode
Median
Mean
4. In the case of negatively skewed frequency distribution curve, mean < median < mode
Mode
Median
Mean
Use of Statistics in Data Science 125

