Weighting Factor

Introduction :

The process of weighting factor involves emphasising some aspects of a phenomenon, or of a set of data — giving them more weight in the final effect or result .The purpose of assigning weighting factors is straightforward  they help us establish work priorities.


Formula to Find Weighting Factor:

Weighting factor includes

Mean     = Sum total number items or values`//` Number of items

Median  = Middle value from a set of values

Mode     =  Frequently occurring items

Range   =Maximum Value`**` Minimum Value

Geometric Mean=`sqrt(AB)`

Weighted Average:

The weighted average or weighted mean is similar to the mean, with one exception. When totaling the each and every individual values, each is multiplied by a weighting factor, and the total is then divided by the sum of all the weighting factors.
Example Problems for Solving Weighting Factor:

1). Find mean, median, mode, range for the following datas

62, 67, 71, 74, 76, 77, 78

Solution:

To find Mean:

Mean = `(67+62+71+74+76+77+78)/(7)`

=`(505)/(7)`

Mean =72.14

To find Median:

Here there totally seven items, in that middle item is 74

Median= 74

To find Mode:

In the above set of items there are no frequently occurring items.

Mode=0

To find Range:

In the above set of values, we have

Maximum value=78

Minimum Value = 62

Range=78`**` 62

Range =16

2) Find the Geometric Mean(G.M) of 3 and 12.

Solution:

The geometric mean means it is a number midway between two values by multiplication

Given A=3, B=12

=`sqrt(3*12)`

G.M=6

3) Find the Weighted average for the following items

Morning class = 62, 67, 71, 74, 76, 77, 78, 79, 79, 80, 80, 81, 81, 82, 83, 84, 86, 89, 93, 98

 

Evening class = 81, 82, 83, 84, 85, 86, 87, 87, 88, 88, 89, 89, 89, 90, 90, 90, 90, 91, 91, 91, 92, 92, 93,   93, 94, 95, 96, 97, 98,    99.

Solution:

If we were to find a straight average of 80% and 90%, we would get 85% for the mean of the two class averages.
The mean for the morning class is 80% and the mean of the evening class is 90%.
This is not the total average of all the students' grades. To find that, you would need to total all the grades and divide by the total number of students.



Steps to find weighted average:

A= Number of students in morning class

B=Mean of morning class

C= Number of students in evening class

D= Mean of evening class

E=Total number of students in both classes

Therefore A=20,B=80,C=30,D=90,E=50

Weighted Average= `(AB+CD)/(E)`

`((20*80)+(30*90))/(20+30)`

=`(4300)/(50)`

Weighted Average =86%

4). Find mean, median, mode, range for the following datas

67, 62, 71, 74, 76, 77, 78, 71

Solution:

Arrange them in ascending order as  62, 67,71,71,74,76,77,78

To find Mean:

Mean =`(62+67+71+71+74+76+77+78)/(8)`



= `(576)/(8)`

Mean =72

To find Median:

Here there are totally eight items, in that middle item is 71 and 74, so we have to take Average.

Median=`(71+74)/(2)`

Median= 72.5

To find Mode:

In the above set of items there are frequently occurring items.

Mode=71

To find Range:

In the above set of values, we have

Maximum value=78

Minimum Value = 62

Range=78`**` 62

Range =16