SuperCalX

Grouped Data Standard Deviation

Calculate the standard deviation for grouped frequency data.
Calculator
Enter your values
Midpoint (x)
Frequency (f)
Analysis
Interpretation of the current calculator output

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How to Use

Step-by-step instructions
  1. 1Enter the midpoint for each group.
  2. 2Enter the frequency for each group.
  3. 3Add more rows as needed.
  4. 4The calculator will compute the mean and standard deviation.

Grouped SD Formula

For grouped data, we use the midpoint (x) of each class and its frequency (f) to estimate the standard deviation.
s = sqrt[(Sum(fx^2) - (Sum(fx))^2/n) / (n-1)]

Variables:

fFrequency
xMidpoint of class
nTotal frequency

Example

Class Data

Inputs:

Group 1:Mid: 5, Freq: 2
Group 2:Mid: 15, Freq: 3

Steps:

  1. 1.n = 5
  2. 2.Sfx = 10 + 45 = 55
  3. 3.Mean = 11
  4. 4.Sum(fx^2) = 50 + 675 = 725
  5. 5.Variance = (725 - 55^2/5) / 4 = (725 - 605) / 4 = 30
  6. 6.SD = sqrt(30) = 5.477
Result:
SD = 5.477

Frequently Asked Questions

How do I find the midpoint?

The midpoint is the average of the lower and upper class limits. E.g., for class 10-20, midpoint is (10+20)/2 = 15.