## Quartiles

Quartiles are the values that divide the data arranged in ascending or descending order into  four equal parts. A distribution is divided into four equal parts by three quartiles.

-   The first or lower quatile (Q1) is the point below which 25% of the items lie and above which 75% of the items lie.
-   The second quartile (Q2) is the point below which 50 percent of the items lie and above which 50 % of the items lie. Of course, the second quartile is the median.
The third (upper) quartile ( Q3 ) is the point below which 75 % of the items lie and above which 25 % of the items lie.

If N be the number of items in ascending or descending order of a distribution then in the case of individual and discrete data,

In case of the grouped data,

Where, L= lower limit of the quartile class
f = frequency of the quartile class
cf = cumulative frequency of preceding class
i = height of class-interval

### Workout Examples

Example 1: Calculate the quartiles from the data: 4, 6, 5, 9, 8, 10, 3

Solution: Here,
Data in ascending order: 3, 4, 5, 6, 8, 9, 10
No. of data (N) = 7

Example 2: Calculate the quartiles from the data: 5, 8, 10, 11, 12, 14, 16, 18, 20, 4

Solution: Here,
Data in ascending order: 4, 5, 8, 10, 11, 12, 14, 16, 18, 20
No. of data (N) = 10

Example 3: Compute Q1 and Q3 from the following data.

 x 5 20 24 29 35 f 2 3 4 3 5

Solution: Here, frequency table,

 x f cf 5 20 24 29 35 2 3 4 3 5 2 5 9 12 17 N = 17

Total number of data (N) = 17

Example 4: Compute Q1 and Q3 from the following data.

 Marks in maths 0-10 10-20 20-30 30-40 40-50 No. of students 5 20 10 15 7

Solution: Here, frequency table,

 Marks (x) f cf 0-10 10-20 20-30 30-40 40-50 5 20 10 15 7 5 25 35 50 57 N = 57

Here, N = 57

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