Statistics

Box Plot Calculator

Find the five-number summary and IQR for a box plot.

Value 1

Value 2

Value 3

Value 4

Value 5

Value 6

Value 7

Calculated Output

Median (Q2) 15.5

Q1 9.75

Q3 21.25

IQR 11.5

Formula: Quartiles via the linear interpolation method

Step-by-Step Breakdown

1. Values used:

2. Value 1 = 4

3. Value 2 = 8

4. Value 3 = 15

5. Value 4 = 16

6. Value 5 = 23

7. Value 6 = 42

8. Value 7 = 0

10. Median (Q2) = 15.5

11. Q1 = 9.75

12. Q3 = 21.25

13. IQR = 11.5

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The math behind it

Sort the data, then find Q1, the median and Q3. IQR = Q3 − Q1 measures the middle 50% spread.

4, 8, 15, 16, 23, 42 → median 15.5, IQR 14.75.

What are the whiskers?

They extend to the furthest points within 1.5×IQR of the quartiles.