Comprehensive Calculator Guide
This calculator gives the minimum share of any data set within k standard deviations of the mean, and the range if you give the mean and SD. Within 2 SDs lies at least 75% of any data. It compares the guarantee with the normal distribution, which packs far more data into the same range.
A floor for any shape
At least 1 − 1/k² lies within k SDs (k > 1). A normal distribution packs far more in: 95.45% within 2 SDs. Use Chebyshev when the shape is unknown or skewed.
How to Use
- Enter k (above 1).
- Optionally enter the mean and SD.
- Press “Calculate” to see the shares and range.
Formula Used
Within ≥ 1 − 1/k² | Range = mean ± k × SD
Practical Examples
- Example 1
- k = 2: ≥ 75%, 50 to 90 for mean 70, SD 10.
- Example 2
- k = 3: ≥ 88.89%.
Important Tips
- Use it for unknown shapes.
- Use the empirical rule for normal data.
- Find the SD first.
Common Mistakes to Avoid
- k ≤ 1.
- Reading the floor as the actual share.
- Confusing it with 68–95–99.7.
Frequently Asked Questions
- What does it say?
- At least 1 − 1/k² within k SDs.
- vs the empirical rule?
- Any shape vs normal only.
- Decimal k?
- Yes, any k > 1.