Measures of Central Tendency or Averages

According to A.L. Bowley, “Statistics may rightly be called as the science of averages.” This average is also known as central value. Through statistical analysis we condense the whole data to a single value, which represents the data in true sense. Thus averages are the values which lie between two extreme values; and it is the reason that these values are known as “Measures of Central Tendency” or “Measures of Location”. These measures are also known as Averages.

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Definitions

Measures of Central Tendency or Averages have been defined differently by different statisticians.

According to Simpson and Kafka, “A measure of Central Tendency is a typical value around which other figures congregate.”

According to A.E. Waugh, “An average stands for the whole group of which it forms a part, yet represent the whole.”

Thus the basic purpose of the statistical analysis is to determine the value which represents the whole series. This value is termed as central value or an average. In other words, average is a statistical measure representing a group of individual values in simple and comprehensive manner.

Objectives and Functions of Averages or Central Value

• The human mind cannot retain all details of large number of activities and their inter-relations, so averages are a must. An average represents all the features of a group, hence the results about the whole group can be deduced from it.
• An average gives us simple and brief description of the main features of the whole data.
• The measures of central tendency or averages reduce the data to a single value which is highly useful for making comparative studies.
• Averages help to develop a business in case of a firm or help the economy of a country to develop. For example, in case of an aviation company, the management will be interested to know about the average number of persons boarding plane on the desired certain route. In such a case, a finance minister or finance secretary would apply some economic measures to increase per capital income if he feels that it is lower as compared to other developed country’s per capital income.
• Other statistical devices such as mean deviation co-efficient of variation, co-relation, analysis of time series and index numbers are also based on the averages; and hence the use of averages becomes compulsory.

Essentials of a good Average

• Only those averages, where all the data are used give best result, whereas the averages which use less data are not representative of the whole group. Averages are not satisfactory where whole of the data are not used.
• No term should affect the average too much. If one or two very small or very large items unduly affect the average then the average cannot be really typical of the entire group. Thus extreme terms may distort the average and reduce its usefulness.
• There should be no confusion about the meaning or description of an average. It must have a rigid or to the point definition. The best thing is that the average should be defined by algebraic formula and the person prejudiced or biased of the investigator should not lead to ill-defining of the average.
• Measures of central tendency are used in many other techniques of statistical analysis like measures of Dispersion, Correlation etc. This purpose can be solved only if measures of central tendency or average are capable of further algebraic treatment.
• That average is considered a good average which can be found by arithmetic as well as by graphic method.
• A good average will be least affected by sampling fluctuations. If a few samples are taken from the same universe, the average should be such as has the least variation in values derived in the individual samples. The results obtained will be considered to be the true representative of the universe in this case.
• We will not call an average good one if it is affected by skew ness present in the distribution.
• A popular average which is known to common people will be more useful as a simple person will be able to understand it. Otherwise its use will be limited to higher section of people only.
• A good average should have a clear and stable definition.