0
The plain arithmetic mean is actually a special case of the weighted mean, except all the weights are equal to 1. The arithmetic mean is the sum of all the individual observations divided by the number of observations. With a weighted mean you multiply each observation by a weight, add those values together and then divide by the sum of the weights.
E.g. Let's say you have 3 observations: 4, 7, 12
The arithmetic mean is (4+7+12) / 3 = 23/3 = 7.67
Now let's assume that you want to weight the first observation by a factor of 10, the second observation by a factor of 5 and the third observation by a factor of 2:
The weighted mean is (4x10+7x5+12x3) / (10+5+2) = 111/17 = 6.53
You can see that if all the weights were 1 you would have the arithmetic mean shown above.
As it is mentioned above arithmetic mean is a special case of weighted mean. In the calculation of arithmetic mean all the observations are given an equal chance of occurance ie
the above mentioned problem can be written as
4*1/3+7*1/3+12*1/3=7.67
or inother words 7.67 is the number it takes if all are given equal chance
whereas in weighted mean the chance of occurance are not equal .This can be written as
4*10/17+7*5/17+12*2/17=6.53
in the above eg. 4 has given more weightage than 7 and 12 has the least weightage so the probability of 4 occurring is more when compared to 7 and 12 there fore the average obtained is seen to decrease as we have given more importance to 4 than others. It shows that the average is affected by the weightage given to the numbers
What else can I help you with?
What is difference between share in shop handling and weighted distribution?
Weighted distribution is the percent of stores that a product is sold in, but weighted by the importance of the outlets, while share in stores handling is the market share of a brand/item just in the stores that stock it.
What is the difference between value weighted index and equal weighted index?
Value weighted index is a market average such as Standard & Poor's 500 Index that takes into account the market value of each security rather than calculating a straight price average. An equal weighted index is a type of weighting that gives the same weight, or importance, to each stock in a portfolio or index fund. The difference is one gives individual value and other gives one value to all.
What statistical concept is used to explain the natural difference that exists between a sample mean and corresponding population mean?
Random error.
What is the difference between axis label and a label in a bar graph?
axis labels are x and y while bar graph labels explain what the graph is representing.
What is the difference between math and arithematic?
Arithmetic is more to do with straightforward number calculations (i.e. multiplying, division, subtraction etc. etc.) Math (or Maths as we call it here in England) involves the whole range of mathematics, such as algebra, geometry, trigonometry, equations and so on.
Is there any difference between expected value and arithmetic mean?
There is. Arithmetic mean is simple average of numbers not weighted by anything. However in EV, the numbers are weighted by their probability
What is the difference between mathematics and arithmetics?
there is no difference between Mathematics and Arithmetic because Arithmetic is a branch of mathematics. there is no difference between Mathematics and Arithmetic because Arithmetic is a branch of mathematics.
What is the common difference?
The difference between each number in an arithmetic series
Difference between round robin scheduling and Weighted round robin scheduling?
One is weighted, the other is not. Simple as.
How is a arithmetic sequence found?
You take the difference between the second and first numbers.Then take the difference between the third and second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Take the difference between the fourth and third second numbers. If that difference is not the same then it is not an arithmetic sequence, otherwise it could be.Keep checking until you think the differences are all the same.That being the case it is an arithmetic sequence.If you have a position to value rule that is linear then it is an arithmetic sequence.
What is a common difference?
The common difference is the difference between two numbers in an arithmetic sequence.
What is the difference between geometric mean and arithmetic mean?
The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
Is The Fibonacci sequence arithmetic?
No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant
What is the difference between an arithmetic series and an arithmetic sequence?
An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.
What is the difference between logical sum and arithmetic sum?
ernycs
How do you explain the difference between the vassals and serfs?
Explain the difference between the vassals and the serfs
How do you determine if a sequence is arithmetic?
The sequence is arithmetic if the difference between every two consecutive terms is always the same.
