Let us understand the concept of Quantile groups and markers

Quantile markers divide the data into equal parts after arranging in ascending order


For example the data set contains scores of 10 students on a test scored out of 100 {5,10,15,20,25,30,35,40,45,50}

In case of 5 quantile groups

1. Each part will contain 20% of the data set i.e 2 values.

2. When you divide the data into 5 quantiles you will get 4 quantile markers (Q1, Q2,Q3 and Q4)

3. The average of 2nd and 3rd value will be Q1 (12.5 for our example)

4. Average of 4th and 5th value will be Q2 (22.5 for our example) and so on (Q3=32.5 and Q4= 42.5)

5. Q1 quantile signals that 20% of the data is less than or equal to that value

6. Similarly Q2 signals 40% of the data is less than or equal to that value and similarly Q3 and Q4


So quantile markers are not just values they are more importantly indicators of the percent of values below or equal to them


Now back to our example

if you add the scores from bottom quantile (5+10) and compare it to a score from top quantile group (45/50), quantity B will be bigger


But if the data set had been {41,42,43,44,45,46,47,48,49,50}

Quantity A would have been bigger


So it all depends on the data set