Range | What is range?

Range | What is range?

Range is the measure of dispersion of the data. Range is given by the difference between two extreme observations of the distribution. If L and S are the largest and smallest observations in a distribution, then the range is L – S. It is denoted by R.

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            Range (R) = L – S

In case of continuous frequency distribution or grouped data, the range is calculated as the difference between the upper limit of the highest class interval and lower limit of the lowest class interval.

Coefficient of Range

We know that the unit of range is same as the unit of the items of the given data. So, two distributions of different units can not be compared with the range. Hence, such two distributions are compared with the help of the coefficient of range. Which is given as,

     

Workout Examples

Example 1: Find the range and coefficient of range from the following data:

                   40, 60, 42, 62, 41, 46, 52, 58, 49, 63, 46, 47

Solution: Here,

                        The largest value (L) = 63

                        And, the smallest value (S) = 40

                        ∴ Range (R) = L – S

                                            = 63 – 40

                                            = 23

                        And,

                        

Example 2: Calculate the range and its coefficient from the following data.

         

Size	4	5	6	7	8	9	10	11
Frequency	2	4	8	9	12	11	7	3

Solution: Here,

                        The largest value (L) = 11

                        And, the smallest value (S) = 4

                        ∴ Range (R) = L – S

                                            = 11 – 4

                                            = 7

                        And,

                        

Example 3: Calculate the range and its coefficient from the following data.      

   

Marks	10-20	20-30	30-40	40-50	50-60	60-70
No. of students	2	4	8	9	12	11

Solution: Here,

                        The largest value (L) = 70

                        And, the smallest value (S) = 10

                        ∴ Range (R) = L – S

                                            = 70 – 10

                                            = 60

                        And,

                        

You can comment your questions or problems regarding the range and coefficient of range here.