SUMMARY- Measures of Central Tendency and Dispersion | Quantitative Aptitude for CA Foundation PDF Download

SUMMARY
The best measure of central tendency, usually, is the AM. It is rigidly defined, based on

all the observations, easy to comprehend, simple to calculate and amenable to

mathematical properties. However, AM has one drawback in the sense that it is very

much affected by sampling fluctuations. In case of frequency distribution, mean cannot

be advocated for open-end classification.
Median is also rigidly defined and easy to comprehend and compute. But median is not

based on all the observation and does not allow itself to mathematical treatment.

However, median is not much affected by sampling fluctuation and it is the most

appropriate measure of central tendency for an open-end classification.
Mode is the most popular measure of central tendency, there are cases when mode

remains undefined. Unlike mean, it has no mathematical property. Mode is also affected

by sampling fluctuations.
Relationship between Mean, Median and Mode

Mean – Mode = 3(Mean – Median)

Mode = 3 Median – 2 Mean
Relation between AM, GM, and HM

AM ≥GM ≥HM

GM and HM, like AM, possess some mathematical properties. They are rigidly defined

and based on all the observations. But they are difficult to comprehend and compute and,

as such, have limited applications for the computation of average rates and ratios and

such like things.