Math and Arithmetic
Statistics

# Is an arithmetic mean a weighted mean or a weighted mean an arithmetic mean?

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###### 2012-12-14 16:49:38

The arithmetic mean is a weighted mean where each observation is given the same weight.

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## Related Questions

There is. Arithmetic mean is simple average of numbers not weighted by anything. However in EV, the numbers are weighted by their probability

The arithmetic mean and the weighted mean are used in different situations. The arithmetic mean is used in frequencies as a general average. The weighted mean is used when different factors contribute to some kind of total for example with weighted index numbers. It is not a matter of accuracy it involves using the right mean in the right situation. Almost always (if not always) a question will specify which mean to use.

The weighted mean is simply the arithmetic mean; however, certain value that occur several times are taken into account. See an example http://financial-dictionary.thefreedictionary.com/weighted+average

The weighted arithmetic mean is used, if one wants to combine average values from samples of the same population with different sample sizes: : The weights wi represent the bounds of the partial sample. In other applications they represent a measure for the reliability of the influence upon the mean by respective values. rhinostar

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

An adjective form is arithmetic, or arithmetical. They mean of or based on arithmetic.

Arithmetic:The computing of numerals and numbers.

1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN &lt; ARITHMETIC MEAN 2.

A weighted mean is when some values contribute more than others. In order to calculate weighted mean multiply each weight by its value, add those and then divide by the sum of the weights.

The arithmetic mean of a single number, such as 1784298281, is the number itself.

Arithmetic is another word for math or mathematics.

weighted mean is getting the weighted average of students. normally, it is always use in computing the general average of the students to determine the ranking of the whole class.

double weightedmean (double runningaverage, double rawdata, double timeconstant) { return runningaverage / (1 - 1/timeconstant) + rawdata / (1/timeconstant); }

You need to have all the values within the range to calculate the arithmetic mean .

arithmetic mean is the average (175+235) / 2 = 205

when is it appropriate to use arithmetic mean as opposed to median

The arithmetic mean of one number, such as 104410231017 is still simply that number.

Two numbers can have only one arithmetic mean. In this case, it is -2.5Two numbers can have only one arithmetic mean. In this case, it is -2.5Two numbers can have only one arithmetic mean. In this case, it is -2.5Two numbers can have only one arithmetic mean. In this case, it is -2.5

Any two numbers can have only one arithmetic mean. If the numbers are x and y, then their arithmetic mean is (x + y)/2.

The answer will depend on how many cases each person can handle. If the handlers all work at similar speeds then an arithmetic mean speed will do both otherwise you will need a weighted average - weighted according to the number of 8-hour shifts that they can put in.

The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".

There are a great number of advantages and disadvantages of Arithmetic mean. One disadvantages is that it is not accurate.

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