Weighted Average Formula

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					                  Weighted Average Formula
Weighted Average Formula

In our day-to-day lives, we have to deal with number crunching, all the time. Be it calculating
exam scores, expenses or statistics of any kind, you need to know rudimentary arithmetic
concepts. Weighted average calculation is quite a simple exercise. In this Buzzle article, I
provide a detailed explanation of how to calculate weighted averages as simply as possible.

What is Weighted Average?

Before I go ahead and explain how to go about calculating weighted average, let us define
and understand what we mean by a weighted average. Its calculation is similar to calculating
the average, but with a slight difference.

The average of a quantity is calculated after summing up all the values of that quantity and
then dividing it by the total number. A weighted average is calculated by taking into
consideration, additional conditions associated with each of the values for the data. That is,
some values are multiplied by an extra multiplicative factor as they occur more often. Unlike
an average value, in which all the values of a quantity contribute equally, in a weighted
average, they contribute unequally. Some values of the particular quantity contribute more
than others and that is why it is called a weighted average.

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Weighted average calculation is an important tool in descriptive statistics and mathematics. If
all quantities are weighted equally or contribute equally, while calculating the weighted
average, it is equal to the arithmetic mean. It comes in handy when you have to combine the
averages of two different sets of values and get an overall average value.

Here is the general formula for weighted average calculation : Weighted Average = (x1 w1 +
x2 w2. .+ xn wn) / (w1 + w2. . + wn) = Σi = 1 to n (xi wi) / Σi = 1 to n wi


Here 'xi' are values of the quantity whose weighted average is being calculated, while 'wi' are
the values of the corresponding weights. So, for calculating weighted average, you must
multiply values of the quantity, with their corresponding weights, add all them up and divide
them by the sum of the weights. Let me explain weighted average calculation through an
example in the next section.

How to Calculate Weighted Average?

To illustrate how to go about weighted average calculation, let me present an example.
Consider the following numbers to be the scores of students in class A of a school: 50, 20, 30,
10, 40, 60, 40, 50,10, 30 and let the following be the scores of students in Class B: 70, 80, 20,
10, 50. The average score of 10 students in class A is 34, while the average score of 5
students in class B is 46. What is the average score of students including both classes?

This can be found out by weighted average calculation. It can be calculated by taking the
weighted mean of the two average scores. The weighted average will be given by : Weighted
Average Score of Both Classes Equal To: [34 (10) + 46 (5)] / [10 + 5] = 38

So, before you make the weighted average calculation, write out the values of the quantity
whose average you plan to calculate along with their corresponding weights. Then simply use
the formula and substitute. Try out problems which ask for weighted average calculation with
percentages, as they are quite interesting to solve.

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                                Find the Median
Find the Median

The Median is the 'middle value' in your list. When the totals of the list are odd, the median is
the middle entry in the list after sorting the list into increasing order. When the totals of the list
are even, the median is equal to the sum of the two middle (after sorting the list into increasing
order) numbers divided by two. Thus, remember to line up your values, the middle number is
the median! Be sure to remember the odd and even rule.

Examples :-

Find the Median of: 9, 3, 44, 17, 15 (Odd amount of numbers)
Line up your numbers: 3, 9, 15, 17, 44 (smallest to largest)
The Median is: 15 (The number in the middle)

Find the Median of: 8, 3, 44, 17, 12, 6 (Even amount of numbers)
Line up your numbers: 3, 6, 8, 12, 17, 44
Add the 2 middles numbers and divide by 2: 8 12 = 20 ÷ 2 = 10
The Median is 10.

The Mode :- The mode in a list of numbers refers to the list of numbers that occur most
frequently. A trick to remember this one is to remember that mode starts with the same first
two letters that most does. Most frequently - Mode. You'll never forget that one!


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Examples:

Find the mode of:
9, 3, 3, 44, 17 , 17, 44, 15, 15, 15, 27, 40, 8,
Put the numbers is order for ease:
3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44,
The Mode is 15 (15 occurs the most at 3 times)

*It is important to note that there can be more than one mode and if no number occurs more
than once in the set, then there is no mode for that set of numbers.

Ocasionally in Statistics you'll be asked for the 'range' in a set of numbers. The range is simply
the the smallest number subtracted from the largest number in your set. Thus, if your set is 9,
3, 44, 15, 6 - The range would be 44-3=41. Your range is 41.

Example 1

Look at these numbers:

3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29

If we put those numbers in order we have:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

There are fifteen numbers. Our middle number will be the eighth number:

3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56

The median value of this set of numbers is 23.


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