Descriptive Statistics

Paste your readings and see their center, spread, shape and normality at a glance.

Is the process stable over time? The order of the readings matters there. Open the I-MR chart

Data · 0 readings
Paste a column from Excel anywhere on this page with Ctrl+V
Paste or upload your measurement data, then hit Calculate to see the full statistical breakdown, histogram, and box plot.

About Descriptive Statistics

How it is calculated · worked example · references

What it does

Paste one column of measurements and get the numbers that describe it: centre (mean and median), spread (standard deviation, variance, range, IQR, coefficient of variation), shape (skewness and kurtosis), confidence intervals for the mean, median and standard deviation, a normality test, and a histogram with a box plot under it.

It is the first look at any data set: before a capability study, to compare a sample with a specification, or to check whether the data are normal enough for the method you want to use next.

Method

Each statistic uses the convention of the specialised statistical packages, so quartiles and skewness can differ slightly from Excel. Normality is checked with the Anderson-Darling test. Every value is checked against an independent statistical library.

Worked example

The data behind “Try an example”: 30 readings around 25.0.

ResultValue
Mean · 95% CI25.0091 · 24.9709 to 25.0473
Standard deviation · 95% CI0.1023 · 0.0815 to 0.1376
Median25.028
Q1 · Q324.947 · 25.077
Normality (Anderson-Darling)p 0.395

The p-value gives no reason to reject normality, so normal-based methods such as Cpk are reasonable. The median sits a little above the mean: a few low readings pull the mean down.

References

  • Montgomery, D. C., Introduction to Statistical Quality Control.
  • Anderson, T. W. and Darling, D. A. (1952), Annals of Mathematical Statistics.