Central tendency is a summary of a dateset through a single value that reflects the centre of the data distribution. It is a part of descriptive statistics.
The central tendency is one of the most important concepts in statistics – and that’s why it also called as measures of the first order.
Importance of Measure Central Tendencies
- A representative value: Measures of central tendency give us one value that represents the entire distribution. It doesn’t give us information about one value; but about the entire distribution.
- Condenses data: Sometimes the data collected may be vast – measure of central tendencies helps us condense the information. It converts the whole set of figures into just one figure and thus helps in condensation.
- Aids in making comparisons: We will need one representative value to compare two set of data. These representative values are found with the help of measures of the central tendency.
- Useful in further statistical analysis: Many techniques of statistical analysis like Measures of Dispersion (Unit 2), Measures of Skewness (Unit 2), Correlation and Regression (Unit 3) are based on measures of central tendency.
Seeing this importance of averages in statistics, Prof. Bowley said “Statistics may rightly be called as science of averages.”
Requisites of ideal measure
According to Prof. Udny Yule, the following are the requirements to be satisfied by an ideal average or measure of central tendency:
- It should be rigidly defined.
- It should be easy to understand and calculate.
- It should be based on all the observations.
- It should be suitable for further mathematical treatment.
- It should be affected as little as possible by fluctuations of sampling.
- It should not be affected much by extreme observations.
Different Central Tendencies
Puzzles
- Choose the odd one out:
- Harmonic Mean
- Median
- Arithmetic Mean
- Geometric Mean
- True or False: Weighted arithmetic mean is a positional central tendency.
Extra Reading Materials
- Descriptive Statistics (link) on Simple Wikipedia
Mathematicos 
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