# Professor Puzzler's Statistics Calculator

Provide a data set below, and find out all you need to know!Outliers Detailed analysisAverageMedianModeRangeStandard deviationHarmonic meanGeometric meanQuartilesIQRVariance# Outliers

*Please enter data above to calculate outliers.*

## Explanation

Outliers are values which are far enough outside the "reasonable" variation of values in a data set that it makes sense to remove them for your calculations.For example, my physics students will use a stopwatch to find out how long it takes a golf ball dropped from the roof of a barn to reach the ground. Now, that is not a long amount of time, and occasionally the student will fumble over the "stop" button, and not get an accurate time reading. Thus, we do several trials, and average the results. But if the results look like this:

*1.20, 1.24, 1.32, 1.15, 1.08, 2.5 (all in seconds)*

It's reasonable to suppose that the 2.5 second reading is an outlier; it is so far off that including it will badly skew our results.

The problem is, we can't just say, "Oh, we'll drop the results that look unreasonable," because that requires us to use our own personal judgment. What's wrong with that? Well, if we don't have a rigorous way of defining outliers, then we may be tempted to drop results simply because doing so gets what we would consider a "better" result.

In other words, we would skew our own results.

Outliers are calculated in the following manner. First the median and quartile values are calculated. The IQR (interquartile range) is then calculated as the difference between the first and third quartile values. The IQR is multiplied by 1.5, and any point which is less than the first quartile, or greater than the third quartile by more than that amount is considered to be an outlier.

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