CHAPTER 4 : MEASURES OF CENTRAL TENDENCY
In the previous chapter, we have studied how to collect raw data, its classification and tabulation in a useful form, which contributes in solving many problems of statistical concern. Yet, this is not sufficient, for in practical purposes, there is need for further condensation, particularly when we want to compare two or more different distributions. We may reduce the entire distribution to one number which represents the distribution.
A single value which can be considered as typical or representative of a set of observations and around which the observations can be considered as Centered is called an ’Average’ (or average value) or a Center of location. Since such typical values tends to lie centrally within a set of observations when arranged according to magnitudes, averages are called measures of central tendency.
In fact the distribution have a typical value (average) about
which, the observations are more or less symmetrically distributed.
This is of great importance, both theoretically and practically.
Dr. A.L. Bowley correctly stated, "Statistics may rightly be
called the science of averages."
The word average is commonly used in day-to-day conversations. For example, we may say that Abert is an average boy of my class; we may talk of an average American, average income, etc. When it is said, "Abert is an average student," it means is that he is neither very good nor very bad, but a mediocre student. However, in statistics the term average has a different meaning.
The fundamental measures of tendencies are:
(1) Arithmetic mean
(4) Geometric mean
(5) Harmonic mean
(6) Weighted averages
However the most common measures of central tendencies or Locations are Arithmetic mean, median and mode. We therefore, consider the Arithmetic mean.
4.2 Arithmetic Mean
4.3 Properties of Arithmetic Mean
4.6 Empirical relation between mean, median & mode