Average Weight
Average Weight
Simple arithmetic mean gives equal importance to al items in a series. In some cases, all the
items in a series may not have equal importance. In such cases the simple arithmetic mean
will not be the suitable average. In such cases, the appropriate average is the Weighted
Average or the Weighted Mean.
The Weighted Average or the Weighted Mean is used when the relative importance of the
items in a series is not same for all items. In this case, each item is judged based on its
relative importance. Weighted Average (Weighted Mean) plays an important role in
Economics.
It has wide applications in finance. Also it is used to calculate Index numbers.Before studying
weighted average we need to know what an average is.
An average is an extremely easy but effective way in place of an entire group by a single
value. Average = \frac{sum\ of\ al \ items\ in\ the\ group}{number\ of\ items\ in\ the\ group}.
Sum of al items in the group means the sum of the values of al the items in the group.
For example find the average of the numbers 133, 124, 49, 64.
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Here the sum of all items = 133 + 124 + 49 + 64 = 370
Number of items = 4.
So the average = \frac{370}{4} = 92.5

Weighted Average Formula
If x1, x2,...xn are the n items and w1,w2,...wn are the corresponding weights allotted to each
item, then the mean is given by = \bar{w} = \frac{w_{1} x_{1} + w_{2} x_{2} + w_{3} x_{3}
+..........w_{n} x_{n}}{N} = \frac{\sum wx}{N} where N = \sumw.
Steps involved in Weighted Average (Weighted Mean) calculations
We take the items as x and the weights as w
Find the product of each item x with the corresponding weight w
Find the total of wx, \sumwx
Find the total weights al otted, \sumw
Weighted Average is calculated using the formula,
Weighted average, \bar{w} = \frac{w_{1} x_{1} + w_{2} x_{2} + w_{3} x_{3} +..........w_{n} x_{n}}
{N}
Situations where we use Weighted Average (Weighted Mean)
Weighted Average (Weighted mean) are used in the fol owing situations.
1. Usual y the importance of all the items in a series is not same. So when the importance of
al the items in a series is not same, we use the weighted average (weighted mean).
2. Weighted averages (Weighted Mean) are the best averages, which can be used in the case
of percentages, rates and ratios.
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3. For comparing the average of one group with the average of another group, when the
frequencies in two groups are different, weighted averages (Weighted Mean) are used.
4. Weighted averages (Weighted Mean) are used in the calculation of birth and death rates.
5. Weighted averages (Weighted Mean) are used to find the index numbers.
6. When the average (Weighted Mean) of a number of series is found out together, the
weighted average is used.
Merits of using Weighted Average
The important merits of using weighted average are given below: -
1. Weighted Average (Weighted Mean) is simple to understand.
2. Weighted Average (Weighted Mean) can be easily calculated.
3. Weighted Average (Weighted Mean) is based on al observations of the series.
4. Weighted Average (Weighted Mean) is capable of further algebraic treatment.
Weighted Average (Weighted Mean) is a good measure of central tendency. It is better to use
weighted averages in many cases where we fail to use the simple averages like arithmetic
mean.
Weighted Average Calculation
Given below are examples to calculate the weighted average
Example 1:
A candidate obtained the fol owing percentages of marks. English 70, Math 90, Stat 75,
Chemistry 88 and Physics 79. Find the weighted average. Given the weights are 1, 2, 2, 3, 3.
Solution
We take the percentage of marks as x values and weights as w. Then we multiply x with the
corresponding w. This total is divided by the sum of the weights. This wil give the Weighted
Average.


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