Question

How do you find the range of the data: 21, 6, 17, 18, 12, 8, 4, 13.

Answer 1

Hint: We first express the given sample inputs in ascending order. Then we express the individual process and formula to find sample range. The modulus value of the difference between the highest and lowest inputs gives the sample range.

Complete step-by-step solution:
The range is calculated by subtracting the lowest value from the highest value while a large range means high variability, a small range means low variability in a distribution.
If in a discrete set the highest and lowest value is $a$ and $b$ respectively then range will be $a-b$.
We have been given a sample of 8 discrete data 21, 6, 17, 18, 12, 8, 4, 13 and we need to find their sample range. In this sample $n=8$.
Arranging them in ascending order we get 4, 6, 8, 12, 13, 17, 18, 21. We consider the inputs as ${{x}_{i}},i=1(1)8$.
We express the mathematical formulas to find those attributes and put the values.
Sample range is equal to the difference between highest and lowest value of the whole sample.
The highest and lowest value of the sample is 21 and 4 respectively.
The difference of them will be the sample range which is $21-4=17$.

Note: These all-required attributes are the measurement of central tendency. The sample range, sample mean, sample median is part of the central tendency. Range provides a quick and rough estimate of the spread of data values within a set.