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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.

Q: Is it the arithmetic mean or weighted mean that is more accurate Why?

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A variable measured at the interval or ratio level can have more than one arithmetic mean.

Mean or more precisely Arithmetic Mean

None of them is "more accurate". They are answers to two different questions.

Technically the mean is more accurate, but it is not always a true representation, when you have a number that is way out of proportion with the rest of the numbers. That is when the median is more useful. See the related question below.

"Average" or "Mean" or, more specifically, "Arithmetic Mean"

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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

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 is more commonly known as the average. It is the sum of the values divided by the number of values.

A variable measured at the interval or ratio level can have more than one arithmetic mean.

A weighted average is a more accurate measurement of scores or investments that are of relative importance to each other. Identify the numbers to be used, identify the weights of each number, convert percentages to decimals, multiply each number by its weight, and add them together to get the weighted score.

There is one arithmetic mean and one geometric mean to a set of numbers.

Short answer: NoLong answer: There is, strictly speaking, no single "mathematic mean" but there is an Arithmetic Mean, a Geometric Mean and a Harmonic Mean (see the related linl for some more details)The "Arithmetic Mean" is what is generally considered the "Average"

Mean or more precisely Arithmetic Mean

None of them is "more accurate". They are answers to two different questions.

The purpose of the weighted mean is to give more importance to some values than others when calculating the average. This is useful when certain values are more significant or carry more weight in the overall dataset.

Technically the mean is more accurate, but it is not always a true representation, when you have a number that is way out of proportion with the rest of the numbers. That is when the median is more useful. See the related question below.

"More Sideways Arithmetic From Wayside School" by Louis Sachar has 96 pages.