Elementary Statistics and Computer Application

Range

• This is the simplest possible measure of dispersion and is defined as the difference between the largest and smallest values of the variable.
 
• In symbols, Range = L – S.
• Where L = Largest value.
• S = Smallest value.
• In individual observations and discrete series, L and S are easily identified.
• In continuous series, the following two methods are followed.

Method 1

• L = Upper boundary of the highest class
• S = Lower boundary of the lowest class.

Method 2

• L = Mid value of the highest class.
• S = Mid value of the lowest class.

Example1

• The yields ( kg per plot ) of a cotton variety from five plots are 8, 9, 8, 10 and 11. Find the range

Solution

• L=11, S = 8.
• Range = L – S = 11- 8 = 3

Example 2

• Calculate range from the following distribution.
• Size: 60-63 63-66 66-69 69-72 72-75
• Number: 5 18 42 27 8

Solution

• L = Upper boundary of the highest class = 75
• S = Lower boundary of the lowest class = 60
• Range = L – S = 75 – 60 = 15

Merits and Demerits of Range
Merits

1. It is simple to understand.
2. It is easy to calculate.
3. In certain types of problems like quality control, weather forecasts, share price analysis, etc.,
4. range is most widely used.

Demerits

1. It is very much affected by the extreme items.
2. It is based on only two extreme observations.
3. It cannot be calculated from open-end class intervals.
4. It is not suitable for mathematical treatment.
5. It is a very rarely used measure.