Weighting Factor

Introduction to weighting factor: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 datas62, 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 haveMaximum value="78" 

Minimum Value = 62Range

="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 multiplicationGiven 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, 98Evening 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 datas67, 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 haveMaximum value="78"Minimum Value = 62Range="78`**`" 62Range =16