How to calculate the Weighted Mean?
The weighted mean is similar to the arithmetic mean. In arithmetic mean each data point contributes equally to the final average but whereas in weighted mean few data points contribute more to the resultant average. Here each data point is associated with some weight. Depending on the weights of observations the contribution in the final average varies.
Weighted mean is a statistical method that is calculated by multiplying the weight by the quantitative outcome associated with it and then adding all the products together. This resultant is divided by the sum of all weights associated with the observations giving a weighted mean. If all the weights of observations are the same then the arithmetic mean is equal to the weighted mean.
Weighted Mean Formula
Let’s consider the data points x1,x2,x3,…,xn which are associated with weights w1,w2,w3,…,wn then the weighted mean can be calculated by the formula-
Weighted Mean = ∑in=1 xi.wi/∑in=1 wi
=(x1w1+x2w2+x3w3+…+xnwn)/(w1+w2+w3+…+wn)
Steps to calculate Weighted Mean
- Tabulate the given data that helps for easy calculations.
- Find wi×xi by multiplying each number with the associated weight.
- Calculate the summation of all products calculated in step-2 to give ∑wi×xi.
- Find the sum of all weights i.e., ∑wi.
- Divide the total value obtained in step-3 ∑wi×xi with the value obtained in step-4 ∑wi to give the final result weighted mean.
Sample Questions
Question 1: Find the weighted mean for the given data
Value
|
Weight
|
10
|
4
|
5
|
3
|
20
|
2
|
15
|
6
|
8
|
10
|
Solution:
Given values associated with weights, calculate ∑wixi and ∑wi to find weighted mean.
xi
|
wi
|
xiwi
|
10
|
4
|
40
|
5
|
3
|
15
|
20
|
2
|
40
|
15
|
6
|
90
|
8
|
10
|
80
|
|
∑wi=25
|
∑wixi=265
|
Weighted mean = ∑wixi/∑wi
= 265/25
= 10.6
Weighted mean for the given data is 10.6
Question 2: Find the weighted mean for the given data
Value
|
Weight
|
5
|
5
|
15
|
2
|
25
|
1
|
Solution:
Given values associated with weights, calculate ∑wixi and ∑wi to find weighted mean.
xi
|
wi
|
xiwi
|
5
|
5
|
25
|
15
|
2
|
30
|
25
|
1
|
25
|
|
∑wi=8
|
∑wixi=80
|
Weighted mean = ∑wixi/∑wi
= 80/8
= 10
Weighted mean for the given data is 10
Question 3: Find the weighted mean for the given data
Value
|
Weights
|
2
|
4
|
4
|
3
|
6
|
2
|
8
|
1
|
Solution:
Given values associated with weights, calculate ∑wixi and ∑wi to find weighted mean.
xi
|
wi
|
xiwi
|
2
|
4
|
8
|
4
|
3
|
12
|
6
|
5
|
30
|
8
|
1
|
8
|
|
∑wi=13
|
∑wixi=58
|
Weighted mean = ∑wixi/∑wi
= 58/13
= 4.46
Weighted mean for the given data is 4.46
Question 4: Find the weighted mean for the given data
Value
|
Weight
|
80
|
0.2
|
90
|
0.4
|
70
|
0.5
|
Solution:
Given values associated with weights, calculate ∑wixi and ∑wi to find weighted mean.
xi
|
wi
|
xiwi
|
80
|
0.2
|
16
|
90
|
0.4
|
36
|
70
|
0.5
|
35
|
|
∑wi=1.1
|
∑wixi=87
|
Weighted mean = ∑wixi/∑wi
= 87/1.1
= 79.09
Weighted mean for the given data is 79.09
Question 5: Find the weighted mean for the given data
Values
|
Weights
|
72
|
2
|
66
|
1
|
76
|
1
|
54
|
4
|
62
|
3
|
Solution:
Given values associated with weights, calculate ∑wixi and ∑wi to find weighted mean.
xi
|
wi
|
xiwi
|
72
|
2
|
144
|
66
|
1
|
66
|
76
|
1
|
76
|
54
|
4
|
216
|
62
|
3
|
186
|
|
∑wi=11
|
∑wixi=688
|
Weighted mean = ∑wixi/∑wi
= 688/11
= 62.54
Weighted mean for the given data is 62.54
Last Updated :
13 Apr, 2022
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