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When data is arranged in ascending or descending order, it can be divided into various parts by different values such as quartiles, deciles and percentiles. These values are collectively called quantiles and are the extension of median formula which divides data into two equal parts. Since the basic purpose of these partition values is to divide data into different parts therefore a relationship exists between them. This relationship is given below and is elaborated with the help of simple problems.

Problem: In a work study investigation, the times taken by 20 men in a firm to do a particular job were tabulated as follows:

Prove that:

### Second Quartile Q2

In case of frequency distribution, quartiles can be calculated by using the formula:

### Fifth Decile D5

In case of frequency distribution, deciles can be calculated by using the formula:

### 50th Percentile P50

In case of frequency distribution, percentiles can be calculated by using the formula:

### Median of Frequency Distribution

In case of frequency distribution median can be calculated with the help of following formula.

Hence it is proved that Q2 = D5 = P50 = Median

In order to see the relationship between Quartiles, Deciles and Percentiles in case of Ungrouped data click here.