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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. Know More About Applied Statistics Math.Tutorvista.com Page No. :- 1/5 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. Learn More Linear Regression Equation Math.Tutorvista.com Page No. :- 2/5 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! Math.Tutorvista.com Page No. :- 3/5 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. Read More About Linear Regression Formula Math.Tutorvista.com Page No. :- 4/5 Thank You Math.TutorVista.com

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posted: | 4/19/2012 |

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