Statistics

Grouped Data Standard Deviation Calculator

Find the mean and SD of grouped (binned) data.

Class 1 midpoint

Class 1 frequency

Class 2 midpoint

Class 2 frequency

Class 3 midpoint

Class 3 frequency

Class 4 midpoint

Class 4 frequency

Calculated Output

Mean 18

Standard deviation 9

Formula: mean = Σ(f·m)/Σf; SD from grouped formula

Step-by-Step Breakdown

1. Values used:

2. Class 1 midpoint = 5

3. Class 1 frequency = 4

4. Class 2 midpoint = 15

5. Class 2 frequency = 8

6. Class 3 midpoint = 25

7. Class 3 frequency = 6

8. Class 4 midpoint = 35

9. Class 4 frequency = 2

10.

11. Mean = 18

12. Standard deviation = Class 1 midpoint + Class 1 frequency = 5 + 4 = 9

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The math behind it

mean = Σ(f·m) ÷ Σf. SD = √(Σf(m − mean)² ÷ N) using class midpoints m.

Classes 5/15/25/35 with frequencies 4/8/6/2 → mean 17.5.

Why use midpoints?

Grouped data loses the exact values, so the class midpoint represents each bin.