Paper 4: Fundamentals of Business Mathematics & Statistic

5.1 MEASURES OF CENTRAL TENDENCY OR AVERAGE

INTRODUCTION :

A given raw statistical data can be condensed to a large extent by the methods of classification and
tabulation. But this is not enough. For interpreting a given data we are to depend on some mathematical
measures. Such a type of measure is the measure of Central Tendency.
By the term of ‘Central Tendency of a given statistical data’ we mean that central value of the data
about which the observations are concentrated. A central value which ‘enables us to comprehend in a
single effort the significance of the whole is known as Statistical Average or simply average.
The three common measures of Central Tendency are :
(i) Mean
(ii) Median
(iii) Mode
The most common and useful measure is the mean. As we proceed, we shall discuss the methods of
computation of the various measures.
In all such discussions, we need some very useful notations, which we propose to explain before proceeding
any further.
(i) Index or Subscript Notation :
Let X be a variable assuming n values x 1 , x 2 , .....x 3 , We use the symbol x j (read “x sub j”) to denote any of
the above mentioned n numbers. The letter j, which can stand for any of the numbers x 1 , x 2 , .....x n is called
a subscript notation of index. Obviously, any letter other than j, as I, k, p, q and s could be used.’
(ii) Summation Notation :

The symbol

n

∑j 1=Xj is used to denote the sum xj’s from j = 1 to j = n. By definition.

n

∑j=1X = x + x + ... + xj 1 2 n

Example 1 :

n

∑j 1= Xj Yj = X 1 Y 1 + X 2 Y 2 + .... + X n Yn

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.1

This Study Note includes

5.1 Measures of Central Tendency or Average

5.2 Quartile Deviation

5.3 Measures of Dispersion

5.4 Coefficient Quartile & Coefficient variation

Study Note - 5

MEASURES OF CENTRAL TENDENCY AND MEASURES OF DISPERSION