12.2 Measures of Location (Central Tendency)

12.2 Measures of Location (Central Tendency)

The measure that gives the centre of the data is called measure of central tendency. Therefore, measure of central tendency is used to find out the middle or central value of a data set.

We have seen that when the raw data has been condensed into a frequency distribution, the information was easily understood. The information given in the data can be further condensed to a single representative value for the entire distribution. It is more or less the central value around which the data appear to be crowded. For example, usually, we make statements such as:

(i) Hassan studies $6$ hours daily.
(ii) The monthly expenditure of Ayesha's house is Rs.$50,000$.
(iii) The speed of Maham's car is $72$ km per hour.
(iv) In a country, yearly income is $70,000$ rupees per head.
(v) The price of onion in the market is Rs.$150$ per kg etc.

If we look at the first statement, we come to know that Hassan does not study exactly $6$ hours daily. Sometimes, he studies more than $6$ hours and sometimes less. But still why do we say that he studies $6$ hours daily? As he studies about $6$ hours daily so in his study time, $6$ hours becomes an important figure because of its approximated statement, which we call Average. Such an average value is known a measure of central tendency because it is a representative value of the daily study time. Similarly, other statements can also be treated as representative values. As each statement locates the centre of a distribution so it is also known as a measure of central tendency.

The following measure of central tendency will be discussed in this section:

(i) Arithmetic Mean (A.M.)
(ii) Median
(iii) Mode
(iv) Weighted mean