# Average Weights by vistateam123

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Average Weights

Simple arithmetic mean gives equal importance to all 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 = sum of all items in the groupnumber of items in the group. Sum of all items
in the group means the sum of the values of all the items in the group.

For example find the average of the numbers 133, 124, 49, 64.
Know More About Irrational Numbers Examples

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Here the sum of all items = 133 + 124 + 49 + 64 = 370

Number of items = 4.

So the average = 3704 = 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 = wˉ = w1x1+w2x2+w3x3+..........wnxnN =
∑wxN where N = ∑w.

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, ∑wx
Find the total weights allotted, ∑w

Weighted Average is calculated using the formula,
Weighted average, wˉ = w1x1+w2x2+w3x3+..........wnxnN
Situations where we use Weighted Average (Weighted Mean)
Weighted Average (Weighted mean) are used in the following situations.

1. Usually the importance of all the items in a series is not same. So when the
importance of all 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 all 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.
Given below are examples to calculate the weighted average

Example 1: A candidate obtained the following 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 will give the Weighted Average.

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