Descriptive statistics calculator

Use the population one when your numbers are every case there is: the grades of everyone in the class, the height of all twelve players on the team. Use the sample one when the numbers are a sample of something bigger and you want to say something about that bigger thing.

The difference is the divisor. The population version divides by n, the sample version divides by n minus 1. With ten numbers that is a gap of more than 5 percent, which is why two calculators can disagree on the same data and both be right.

This tool shows both instead of picking one quietly, because a result that does not say which definition it used cannot be checked.

Because quartiles have more than one definition, and both are in common use. This tool interpolates linearly at position (n-1)p, which is what Excel's QUARTILE.INC, PERCENTILE.INC and the numpy default do.

The other common convention uses (n+1)p and appears in Excel as QUARTILE.EXC. On the same series the two give different numbers. Neither is wrong; the mistake would be not saying which one was used.

By Tukey's rule: anything below the first quartile minus one and a half times the interquartile range, or above the third quartile plus the same amount, is drawn as a separate point.

That is also why the whisker does not always reach the smallest and largest values. It stops at the furthest point that is still inside the fence, which is the part people get wrong when drawing the plot by hand.

Choose the comma in the decimal separator field. With the comma selected it stops being a separator between values, so 3,5 stays one number and you separate the values with spaces, line breaks or semicolons.

The field is a choice instead of a guess on purpose. In Portuguese, 3,5 is one number and 3, 5 is two, and no automatic rule can read both correctly without breaking the other.