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Confidence Interval of the Mean

Calculate the sample mean and its confidence interval (lower to upper) with the t distribution. Change the confidence level box under the result and the interval updates immediately.

1Data Table

Paste a table copied from Excel into a cell (Ctrl+V). Click a column header (A, B…) before pasting to use the first line as column names. Double-click a header to rename it, right-click to insert/delete rows and columns, and formulas such as =A1*2 work too.

2Confidence Interval Options

Select the columns for the confidence interval (multiple allowed):

How to calculate a confidence interval

  1. Copy the measurement columns together with the header.
  2. Click the column header (A) in the data table and paste - the first line becomes the column name. You can also open a CSV or Excel file.
  3. Select the columns (each column gets its own table).
  4. Press Analyze and check the table and interpretation. Changing the confidence level (%) applies immediately.

How it is calculated

The interval for the mean with an unknown population standard deviation: sample mean ± t(1-α/2, n-1) × s/√n, where s is the sample standard deviation (n-1) and n the number of valid values. Fewer than 2 values cannot give an interval.

Confidence level

The default is 95% and it can be set from 1% to 99.9% in 0.1% steps. A higher level gives a wider interval; more data give a narrower one.

How to read a confidence interval

  • A 95% confidence interval means that if samples were drawn repeatedly the same way, about 95% of the intervals would contain the true mean.
  • If the target or spec center lies outside the interval, the mean has probably shifted from the target (the formal test is the 1-sample t test).
  • If the interval is too wide, collect more data or reduce the measurement spread.

Frequently asked questions

Why the t distribution instead of the normal (Z)?

Because the population standard deviation is unknown and estimated from the sample. With many values the two are almost identical.

Is it the same as in descriptive statistics?

Yes - the same calculation as '95% CI for mean' in the descriptive statistics table, but here you can change the level.

Can I copy the result?

Right-click the result table and choose 'Copy table' to paste it into Excel.

Is my data sent to a server?

No. All calculations run inside your browser and nothing is transmitted or stored.

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