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Range (Max minus Min)

R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}

Worked example: high 98, low 62 → range 36 — press Try an example to run it live, then adjust anything.

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Grade 12Grade 12 Math

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Range (Max minus Min) explained

Rxminxmax

The range is spread at its crudest: highest minus lowest, no averaging, no squares. Daily weather reports live on it — a high of 98 °F and a low of 62 °F is a range of 36 degrees — and quality engineers still use it on the shop floor because an operator can compute it in their head. It is also the basis of the handy field estimate that a standard deviation is roughly the range divided by four for moderate samples, useful when you need a σ to plug into a sample-size calculation and have nothing else.

The fatal weakness is that it depends on exactly two numbers and ignores everything in between, so a single mis-keyed value destroys it. Worse, the range grows systematically with sample size: draw 10 values from a distribution and you might span 3σ, draw 1,000 from the same distribution and you will span more like 6σ, even though nothing about the population changed. That makes ranges from different-sized samples incomparable — one reason the interquartile range, which trims the extremes away, is preferred whenever you have enough data to compute it.

Range (Max minus Min) formula

R=xmax⁡−xmin⁡R = x_{\max} - x_{\min}
Where
  • RR= Range
  • xmax⁡x_{\max}= Maximum value
  • xmin⁡x_{\min}= Minimum value

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