Variance Calculator
On each line, write one value (x) and its frequency (f), separated by a comma — a full frequency table (fx, deviations, f x deviation²) is built and the variance (grouped data) comes out. For ungrouped data, write frequency 1 for each value.
| x | f | fx | x - mean | (x - mean)² | f (x - mean)² |
|---|---|---|---|---|---|
| Enter data. | |||||
How to use
- Write a value and frequency on each line, for example: 10, 3 means value 10 appears 3 times.
- The table shows each row's fx, difference from the mean, its square, and the frequency-multiplied value.
- The summary below shows N, sum fx, mean, population variance and sample variance.
Tips
- For a simple ungrouped list, like test scores, write 1 as the frequency for every value.
- Use population variance when your data is the whole group, and sample variance when it is a subset drawn from a larger group.
- A very large variance often means an outlier or a typing mistake — check the table rows before trusting the summary.
Note: Population variance = sum of f(x - mean)² / N. Sample variance has the denominator (N - 1). For class intervals, write the class mid-point (mark) instead of x.
Frequently Asked Questions (FAQ)
How do I enter data in the variance calculator?
Write one value and its frequency per line, like 10, 3; for ungrouped data use frequency 1 for each value.
What does the table show?
It builds a full frequency table with fx, deviations and squared deviations, and shows the population and sample variance.
Does it show population or sample variance?
Both. Population variance divides by N and sample variance divides by N minus 1; the table shows the steps for each.
Can I use it for grouped class intervals?
Yes. For class intervals, enter the class mid-point instead of the raw value on each line.