# What does range in descriptive statistics mean

What does high range in my variable mean??. If I have a variable whose range is less ,what does it mean??

## 1 Answer

Range in statistics is defined as

$$\operatorname{Range}(X) = \max(X) - \min(X)$$

I you divide the range by $$2$$, you get mid-range, one of the measures of the central tendency. Notice that for some software, for example R, what is returned are minimum and maximum (so the data "ranges" from minimum to maximum).

Alternatively, what may be meant is the interquartile range

$$\operatorname{IQR}(X) = q_{0.75}(X) - q_{0.25}(X)$$

where $$q_{0.75}, q_{0.25}$$ are third and first quartiles respectively. The second case is the range of the $$50\%$$ "middle" of the data.

In both cases those ranges tell you how spread your data is. The definition using minimum and maximum would obviously be heavily influenced by the extreme values, this may be helpful feature, or misleading property, depending on the nature of the data and your analysis purpose.

• If I have a variable whose range is 10 and same variable with range 5. Which variable should I choose??.Either tye variable with range 10 or range 5? – Anees May 22 '19 at 6:28
• @Anees choose for what purpose? Why would you like to choose it based on range? – Tim May 22 '19 at 6:29
• It is a question asked to me. If I was given 3 set of data sets(n=10) with ranges 5-10, 5-50,5-8. Which dataset would you choose and why? – Anees May 22 '19 at 6:33
• Thanks for you answers. So with range we can't decide if that dataset is good or bad, that is what I understood – Anees May 22 '19 at 7:46
• @Anees yes, same as with any other descriptive statistic, they just "describe" how it is. – Tim May 22 '19 at 7:49