Statistics

Quartile Calculator

Find the quartiles of a data set.

Value 1

Value 2

Value 3

Value 4

Value 5

Value 6

Value 7

Calculated Output

Q1 11

Q2 (median) 36

Q3 39.5

IQR 28.5

Formula: Quartiles by linear interpolation

Step-by-Step Breakdown

1. Values used:

2. Value 1 = 6

3. Value 2 = 7

4. Value 3 = 15

5. Value 4 = 36

6. Value 5 = 39

7. Value 6 = 40

8. Value 7 = 41

10. Q1 = 11

11. Q2 (median) = 36

12. Q3 = 39.5

13. IQR = 28.5

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The math behind it

Q1, Q2 (median) and Q3 sit at the 25th, 50th and 75th percentiles. IQR = Q3 − Q1.

6, 7, 15, 36, 39, 40, 41 → Q1 11, Q2 36, Q3 39.5.

What is the IQR for?

It measures spread and helps flag outliers (beyond 1.5×IQR).