Range

Range

Raw Data:

Range is defined as difference between the largest and smallest observations in the data set. Range(R) = Largest value in the data set (L) –Smallest value in the data set(S)

R= L - S

Grouped Data:

For grouped frequency distribution of values in the data set, the range is the difference between the upper class limit of the last class interval and the loawer class limit of first class interval.

Coefficient of Range

The relative measure of range is called the coefficient of range.

Co efficient of Range = (L-S) / (L+S)

Example 6.2

The following data relates to the heights of 10 students (in cms) in a school.

Calculate the range and coefficient of range.

158, 164, 168, 170, 142, 160, 154, 174, 159, 146

Solution:

L=142 S=174

Range = L – S = 174 – 142 = 32

Coefficient of range = (L-S)( L+S)

=(174-142)/(174+142) = 32/316 = 0.101

Example 6.3

Calculate the range and the co-efficient of range for the marks obtained by 100 students in a school.

Solution:

L = Upper limit of highest class  = 75

S = lower limit of lowest class = 60

Range  = L-S = 75-60 = 15

Coefficient of range = (L-S)( L+S)

=15/(75+60) = 0.111

Merits:

·           Range is the simplest measure of dispersion.

·           It is well defined, and easy to compute.

·           It is widely used in quality control, weather forecasting, stock market variations etc.

Limitations:

·           The calculations of range is based on only two values – largest value and smallest value.

·           It is largely influenced by two extreme value.

·           It cannot be computed in the case of open-ended frequency distributions.

·           It is not suitable for further mathematical treatment.