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How are the measures of central tendency and measure of dispersion complementary to each other in descriptive statistics?
in Data Science & Statistics by Platinum (119,120 points) | 600 views

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Only reporting on the avergae is not enough as it only give the typical numbers but does not shed any light on the shape of the distribution thus the need to have both types of measures when doing descriptive statistics.



To fully appreciate the complementary nature between measures of central tendency and measures of dispersion in descriptive statistics, it is important to understand why we we do descriptive statistics in the first place.

Descriptive statistics are summary indicative numbers that represent what is happening in the data. The show us the typical numbers in the form of averages like mean, median and mode, whilst the distribution of points around these averages is important to understand the shape of the data.

Now if I just report on the average it robs us of the information of how the data was distributed.


Simple  example:

If I have two datasets $A=\{1,2,3\}$ and $B=\{2,2,2\}$ then the mean ($\bar{x}$) is equal to $2$ for both data sets but these two sets are not the same in terms of of distribution thus the average alone is not enough and needs to be supplemented by a measure of dispersion like range, inter-quartile range, standard deviation or variance.

so for set $A$

$\bar{x} =2$

Median = 2

The 3 Modes are: 1, 2, 3

Range = Maximum - Minimum = 3 - 1 = 2

for set $b$

Mean = Median = Mode = 2

Range = 2 - 2 = 0

Stock Price Volatility Example


The above diagram shows the historical volatility of two stocks. They both have an average stock price of $100 but differ in their stability (variance/standard deviation). The black stock is consistent arounf the average amount whereas the blue stock fluctuates way above and below the average. So telling someone the average alone will not help them make informed decisions based on historical data.

by Platinum (119,120 points)

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