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.
Calculator
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Midpoint (x)
Frequency (f)
Analysis
Interpretation of the current calculator output
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How to Use
Step-by-step instructions
- 1Enter the midpoint for each group.
- 2Enter the frequency for each group.
- 3Add more rows as needed.
- 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:
fFrequencyxMidpoint of classnTotal frequencyExample
Class Data
Inputs:
Group 1:Mid: 5, Freq: 2
Group 2:Mid: 15, Freq: 3
Steps:
- 1.n = 5
- 2.Sfx = 10 + 45 = 55
- 3.Mean = 11
- 4.Sum(fx^2) = 50 + 675 = 725
- 5.Variance = (725 - 55^2/5) / 4 = (725 - 605) / 4 = 30
- 6.SD = sqrt(30) = 5.477
Result:
SD = 5.477