Average Weight

Average Weight Average Weight 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 = \frac{sum\ of\ all\ items\ in\ the\ group}{number\ 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.

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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 allotted, \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 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.

Weighted Average Calculation 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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