Repeated Observation Mean and Spread Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Repeated readings
Use the same units for every reading. Runs in your browser — nothing is uploaded.
Mean & spread
Paste your repeated readings to see the statistics.
How to use this calculator
- Paste or type your repeated readings of the same quantity, separated by commas, spaces or new lines.
- Keep the units consistent across every reading.
- Read the mean, the spread (standard deviation), the standard error and the largest residual.
How it works
The tool averages your readings and describes their spread using the sample standard deviation (n−1), which is the right estimator when your readings are a sample of all possible measurements.
The standard error (s/√n) is the spread of the mean itself — it shrinks as you take more readings. The largest residual (the biggest difference from the mean) helps you spot a possible blunder to reject and re-measure.
Worked example
Five distance readings. 10, 12, 11, 13, 14 give a mean of 12, a sample standard deviation of about 1.58, a standard error of about 0.71, and a largest residual of 2.
Tips
- More readings tighten the mean (standard error falls with √n), but they can't fix a systematic error — only a better procedure can.
Frequently asked questions
Sample or population standard deviation?
This uses the sample standard deviation (divides by n−1), the usual choice for a set of repeated observations. The population version (÷ n) is only correct when your readings are the entire population, which is rarely the case in survey work.
How do I decide whether to reject a reading?
Compare the largest residual to the spread of the set and your survey tolerance. A reading far outside the others is a candidate blunder — investigate and, if justified, remove it and re-measure rather than just averaging it away.
Is this official course material?
No. It is free study support mapped to surveying course levels — not official North Metropolitan TAFE content or advice. Always follow your lecturer and the official assessment brief, and check your own working.
Related tools
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.