## MEASURES OF CENTRAL TENDENCY BCOM 1ST YEAR

### QUESTION: What is statistical Average? State the properties of good average?

Average is a statistical measure representing a group of individual values in simple and comprehensive manner.

ACCORDING TO CLARK

“Average is an attempt to find one single figure to describe whole of figures”.

ACCORDING TO LEABO
“The average is sometimes described as a number which is typical of the whole group.”

According to Ya Lun Chou

Average is a typical value in the sense that it is sometimes employed to represent all the individual values in a series or of a variable.

#### PROPERTIES OF A GOOD AVERAGE

According to Prof. Yule and Kendall, an average should possess the following properties

• (1) Should be rigidly defined,
• (2) based on all observations,
• (3) easy to understand,
• (4) easy to compute,
• (5) least affected by fluctuations of sampling,
• (6) capable of further algebraic treatment,
• (7) Not/unduly affected by extreme items,
• (8) can be located graphically,
• (9) capable of being used in ‘further statistical computation.

Rigidly Defined. It means, everyone finds the same results. If an average is left to the observer and if it is not definite value then it cannot be representative of the series. If the investigator is biased, the value of the average would be definite and stable. In brief, we can say that the average should lead to one and only one interpretation by different persons. It means the definition should not be left to the will of the investigator. If it is left to the observer, then its value would not be definite and fixed. To solve this problem average should be defined by algebraic formula, which can universally be recognized.

Based on All Items: An average will not be representative if some of the items of the series are excluded from the group. There are some averages which do not take into account all the values of a group. Such averages cannot be satisfactory averages. A good measure should take into account all observations of a group.

Easy to Calculate and Follow: In case the calculation of an average involves too much mathematical processes, it will not be easily understood and its use will be confined only to a limited number of persons and hence, this average cannot be a popular average. It should be easy to understand so that its meaning can be made clear even to a layman. The important quality of good average is that it should not be too mathematical and its calculation should not be too difficult. The mere knowledge of plus, minus, division and multiplication should be required.

Not Affected by Variations of Sampling: The difference in the values of the averages for different samples is called fluctuations of sampling. If in a specific field, two independent sample studies are made, the average should not differ much. But when two independent enquiries are made, there is bound to be a difference in the average values. The average values in some cases would be more whereas in case of others it may be less. If the fluctuation of sampling’ is less, then that average will be regarded better than those where the difference is more.

Capable of Further Algebraic Treatment: If an average does not enjoy this quality, then its use is bound to be very limited. In that case, it may not be possible to calculate combined average of two or more than two from their individual averages. Besides, it will not be possible to study the average relationship of different parts of a variable if it is expressed as the sum of two or more variables. That means a good average should be amenable to further algebraic treatment.

Affected by Extreme Items: In average, each and every item should affect the value of the average. No item should affect the average unduly. If one or two very small very large items unduly affect the average, in that case average cannot be typical of the complete group. That way extreme items may distort the average and adversely affect it.

Not affected by skewness: A good average is the one which is not affected by skewness in the distribution. Contrary to this, if it is affected by skewness, it cannot become a true representative.

Average can be found by Graphic Method: A good average is one which can be found by arithmetic as as graphic method.