R Bar Statistics

The r- bar Statistics is the science of creating ordered use of arithmetic data between the groups of individuals. The r-bar statistics deals with all features of this, jointly with not only the group, study and understanding of such data, but also the planning of the collection of data. The r-bar is the average range of set observations. The r-bar statistics is mainly used to find the average range between the groups of data series. Range measures variability of process.


Formula to Find R Bar Statistics:

Range is defined as the difference between the Maximum value to the Minimum value.

Range=Maximum value – Minimum value

R-Bar defined as the average range of set of observations

R-bar (Average range) is defined as
R-Bar =` ("Range1" + "Range2") / 2`
Coefficient of range is defined as
Coefficient of range = `("MaxValue"** "MinValue") / ("MaxValue" **" MinValue")`
Example Problems for Solving R Bar Statistics:

Example1:

Find out the r-bar (average range) for the following datas?

Series1:  2, 5,9,14,17,23,39.

Series2: 13,17,23,28,35,45,49

Solution:

Range for series1 is

Here the maximum value=39, minimum value=2

Range=Maximum value – Minimum value

=39-2

=37

Range for Series2 is

Here the maximum value=49, minimum value=13

=49-13

=36

R-bar = `("Range1"+"Range2")/2`

= `(37+36)/2`

R-bar =36.5

Example2:

Find out the r-bar (average range) for the following datas?

Series1:  10, 13, 15, 19,21,25,28

Series2: 13,17,19,22,25,27,29

Solution:

Range for series1 is

Here the maximum value=28, minimum value=10

Range=Maximum value – Minimum value

=28-10

=18

Range for Series2 is

Here the maximum value=29, minimum value=13

=29-13

=16.

R-bar = `("Range1"+"Range2")/2`

= `(18+16)/2`

R-bar =17

Practice problems for solving r bar statistics:

Problem1:

Find out the r-bar (average range) for the following datas?

series1: 12, 23,32,40,55,65,78,90.

series2: 10, 20, 36, 92, 95,40,50,56

Answer: 62

Problem2:

Find out the r-bar (average range) for the following datas?

series1: 50        56        80        70        60        60        88.

series2:   36        92        95        40        50       56        80

Answer: 48.5