In a data set the median is the middle part of it. It means it divides the data in two different parts. But, quartiles divide an array or data set in four parts. If you go with Dectiles, then division of arrays takes place in ten parts. This clears that percentiles which means hundred divides an array into hundred parts.

In quartiles as the array divides into four parts so, the second part of that array will always be the value of the Median.

For the lower quartile or the first quartile the formula is used as

Quartiles dectiles and percentiles are the important part of the statistics 1

For the above formula

L is the lower limit of Q1

f is the frequency of that class

h is the width of that class

C is the cumulative frequency

With the above formula you can also find out the 3rd quartile as

Quartiles dectiles and percentiles are the important part of the statistics 2

In the same way the Dectiles can be obtained with

Quartiles dectiles and percentiles are the important part of the statistics 3

So, it is very simple for anyone observing each Dectile. The upper limit is always 9. For a percentile the formula needs to be used is–

Quartiles dectiles and percentiles are the important part of the statistics 4

The upper limit for percentile is always 99.

Now, anyone can get the difference of quartiles, Dectiles and percentiles. However, for each section the value gets changed according to the particular class. So, For the Dk  class containing Dectile the cumulative frequency > (k*N) /4.

In the same way for Pk the cumulative frequency > (k*N) /100.

With the proper knowledge of this the student or the observer can easily find out the particular data or record related to a specific statistical array.

Example 6. Determine (a) Q1, (b) Q3 , (c) D5 (d) P80 from the following distribution :

Quartiles dectiles and percentiles are the important part of the statistics 5
Quartiles dectiles and percentiles are the important part of the statistics 6
Quartiles dectiles and percentiles are the important part of the statistics 7
Quartiles dectiles and percentiles are the important part of the statistics 8Quartiles dectiles and percentiles are the important part of the statistics 9Quartiles dectiles and percentiles are the important part of the statistics 10Quartiles dectiles and percentiles are the important part of the statistics 11Quartiles dectiles and percentiles are the important part of the statistics 12Quartiles dectiles and percentiles are the important part of the statistics 13Quartiles dectiles and percentiles are the important part of the statistics 14Quartiles dectiles and percentiles are the important part of the statistics 15Quartiles dectiles and percentiles are the important part of the statistics 16Quartiles dectiles and percentiles are the important part of the statistics 17Quartiles dectiles and percentiles are the important part of the statistics 18

 

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