MEASURE OF CENTRAL TENDENCY
What:-
The methods of finding out the central or average value of a statistical series.
Why?
1. It’s not possible to remember each and every fact and observations to a field of enquiry.
2. Summary: It provides a single value that summarizes the entire dataset, giving a quick overview of its central tendency.
3. Interpretation: Helps in interpreting data by identifying the most representative or typical value.
4. Comparison: Facilitates comparison between different datasets or groups by providing a common reference point.
5. Decision-making: Aids in decision-making processes by providing insights into the central value around which data is distributed.
6. Detection of outliers: Helps in identifying outliers or extreme values that deviate significantly from the central tendency.
7. Stability: Measures of central tendency are less sensitive to fluctuations in individual data points, providing a stable reference point.
8. Forecasting: Can be used in forecasting future trends or making predictions based on historical data.
9. Data Reduction: Simplifies complex datasets into single values, making it easier to communicate and analyse.
Characteristics :-
There are various types of averages viz. Mean, Median, Mode, Geometric Mean, Harmonic Mean ete. having different characteristics along with their merits and demerits.
But an average to be considered an ideal one, it should bear the following characteristics:
1. It should be rigidly defined. This characteristic requires that an average should have a definite meaning and that it should leave no room for ambiguity, or misunderstanding. For this purpose, it should have an algebraic formula for its computation.
2. It should be simple to understand. This characteristic requires that the meaning, and nature of an average should be such that a man of ordinary prudence can easily understand it.
3. It should be simple to calculate. This characteristic requires that the procedures involved in the calculation of the average value should be very simple, and free from mathematical intricacies.
4. It should be based on all the observations of the series. This characteristic requires that an average should be calculated after taking into account all the items of the series. This is because, an average is supposed to represent all the values of a series.
5. It should be capable of making relative study. This characteristic requires that an average should be such that in its calculation, it should take into account the relative changes in a phenomenon viz price level.
6. It should be capable of further algebraic treatment. This characteristic requires that an average should be such that it enables an analyst to make more, and more mathematical analysis on the basis of its result. For this, the average should have a well-built mathematical model.
7. It should not be greatly affected by the values of extreme items of a series. This characteristic requires that the method of calculation of the average should be such that its value would not be greatly affected by the values of one, or two very great, or small values of the series. If, few extreme values of the series are able to influence very much the value of the average, then such average will not be the true representative of the series.
8. It should not be affected by fluctuations in sampling. This characteristic requires that if sample data are collected from a particular population, or universe at different times, or for number of average value of each sample should not be very much different from each other. Such averages whose values are not affected very much by the fluctuation, or change in sample study are taken as ideal ones.
