Calculator Form
Use raw observations or a frequency table. The form stays in one main page flow, while fields adapt to screen size.
Formula Used
The calculator applies the sample variance formula for a dataset with at least two observations.
s² = Σ(xᵢ − x̄)² / (n − 1)
Where x̄ is the sample mean, n is the number of observations, and Σ(xᵢ − x̄)² is the sum of squared deviations.
For frequency tables, the same idea becomes s² = Σ[f(x − x̄)²] / (n − 1). The divisor n − 1 is Bessel’s correction, which makes the estimate more reliable for samples.
How to Use This Calculator
- Enter a dataset name to label your result sheet.
- Select Raw data list for individual values or Frequency table for repeated values.
- Choose the number of decimal places for display.
- Type values separated by commas, spaces, or line breaks.
- Press Calculate Sample Variance to show the result above the form.
- Review the summary tiles and the detailed working table.
- Use the export buttons to download a CSV summary or PDF report.
Example Data Table
A quick classroom example using five observations with mean 10 and sample variance 2.5.
| Observation | Value | Deviation from Mean | Squared Deviation |
|---|---|---|---|
| 1 | 8 | -2 | 4 |
| 2 | 10 | 0 | 0 |
| 3 | 12 | 2 | 4 |
| 4 | 9 | -1 | 1 |
| 5 | 11 | 1 | 1 |
| Total Squared Deviations | 10 | ||
| Sample Variance | 10 / (5 - 1) = 2.5 | ||
Frequently Asked Questions
1. What does sample variance measure?
Sample variance measures how far sample values spread around the sample mean. Larger values indicate greater dispersion, while smaller values show tighter clustering around the average.
2. Why does the formula use n − 1?
Using n − 1 applies Bessel’s correction. It reduces bias when estimating population variance from a sample, especially for smaller datasets used in education and introductory statistics.
3. Can I enter decimals and negative numbers?
Yes. The calculator accepts integers, decimals, and negative values. It treats them as numeric observations and computes the mean, deviations, and sample variance accordingly.
4. When should I use frequency mode?
Use frequency mode when several observations repeat. Instead of listing every value individually, enter each distinct value once and provide how many times it occurs.
5. What is the difference between variance and standard deviation?
Variance is the average squared spread using n − 1. Standard deviation is the square root of variance, so it returns dispersion in the original data units.
6. How many values do I need?
You need at least two observations. With only one value, the denominator becomes zero, so sample variance is not defined.
7. Does the calculator also show supporting statistics?
Yes. It reports sample size, mean, sum, sum of squared deviations, standard deviation, standard error, range, minimum, maximum, and coefficient of variation.
8. Is this calculator suitable for classroom assignments?
Yes. It is designed for educational use, supports step-by-step review, and provides export tools for worksheets, study notes, and result sharing.