As you know median is the middle value of the variable when the items are arranged in the order of magnitude. Thus, median splits the series into two equal parts. Hence, it is called positional average. In fact there are other positional measures that partition the series into still more number of equal parts, say four equal parts or 10 equal parts or 100 equal parts. Such measures are generally known as Partition Values. There are three partition values:
1) Quartiles, 2) Deciles and 3) Percentiles, which are in much use. They are, of course, the measures of non-central location. Now, let us study about them one by one.
Note: You must keep in mind that the procedure for calculation of these partition values is same as the procedure of median. However, application is slightly differ. You should try to understand the procedure of expressions carefully by comparing the expressions of the median.
Quartiles
The values of a variate that divide the series or the distribution into 4 equal parts are known as Quartiles. Since three points are required to divide the data into 4 equal parts, we have three quartiles Q1, Q2 , and Q3 .
The first quartile (Q1), known as a, lower quartile, is the value of a variate below which there are 25% of the observations and above which there are 75% of the observations.
The second quartile (Q2 ) is the.value of a variate which divides the distribution into two equal parts. It means, there are 50% observations above it and 50% below it. Therefore, Q2 is the same as median.
The third quartile (Q3 ), known as an upper quartile,'is the value of a variate below which there are 75% observations and above which there are 25% observations.
It is clear that Q1 < Q2 < Q3
Deciles
The values of a variate that divide the series or the distribution into 10 equal parts are called Deciles. Each part contains 10% of total observations. Obviously there should be nine such values denoted as D1 , D2.....D9. They are called first decile, second decile, etc. The 5th decile (D5 ) is the median.
Percentiles
The value of a variate which divides a given series or distribution into 100 equal parts are known as percentiles. Each percentile contains 1% of the total number of observations. The percentile P. is that value of the variate upto which lie exactly j % of the total number of observations. For example:
P10 = Value of a variate upto which lies exactly 10% of observations. This is same as D1 .
P20 = Value of a variate upto which lies exactly 20% of observations.
P25 = Value of a variate upto which lies exactly 25% of the total number of observations. This is same as Q1 .
P30 = Value of a variate upto which lies exactly 50% of the total number of observations. This is the same as D5 or Q2 or median.
Similarly, P75 = Q3
