TechnoBlot

The Measure of Central Tendency

A measure of central tendency can be generally defined as the value that tends to describe the set of data by locating the central position within the set of data.

Icons of Measures
Mean which can be defined as the average of something is generally used to measure the central tendency, but in some other cases, other parameters like mode and median can also be used for the measures of central tendency.

  • Arithmetic Mean
  • Median
  • Mode
  • Geometric Mean
  • Harmonic Mean
  • Weighted Mean

A simple diagram to explain what they are in general

A Measure of Central Tendency


                                 Median                     Mean                     Mode

                  The middle value of data         Average     Most commonly occurring value

Mean (Average)

Mean value generally denotes the centre of the distribution. The mean is generally calculated by the sum of all the values and getting it divided by the total number of values in the set.

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It is generally affected by extreme values. This is one of the disadvantages of the mean value.
The advantages of calculating the mean are it is easy to understand and are easy to calculate. They can be subjected to any kinds of further mathematical calculations.

Median
Median is generally calculated by arranging all set of data from the lowest to highest values and taking the data that generally lies in the middle of the sequence.

  • If n is odd, then generally take the middle value.
  • If n is even, then generally take the average of two middle values.

This is the only way that can be used while dealing with qualitative data. It can be easily determined graphically.

Mode
The mode can be defined as the most frequently occurring value in the data set. The tricky thing is that there can be several modes or in some cases no modes at all.

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The above diagram locates the existence of no mode value and 1 or 2 mode values.
Whereas for the grouped data mode can be calculated by the below formula,

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Fm is generally the mode frequency.
F1 is the frequency lower mode class.
F2 is frequency after mode class.
C is generally the class difference.

Reference

https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php

https://statisticsbyjim.com/basics/measures-central-tendency-mean-median-mode/

http://onlinestatbook.com/2/summarizing_distributions/what_is_ct.html

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