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Is a sum of averages accurate?

Updated: 9/23/2023
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10y ago

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No, a sum of averages is NOT as accurate as the average of the whole.

For example:

A=avg (1,10) = 5.5

B=avg (1, 1, 1, 1, 1) = 1

avg(A,B) = 3.25 [Average of averages]

avg(1,1,1,1,1,1,10) = 2.29 [The original data set]

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Q: Is a sum of averages accurate?
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How do you calculate an overall average from a set of component averages?

I recommend you do not try to average a set of components, because your result may be not be accurate. The best way to find an overall average is to average the entire data set.EXAMPLE: You have three columns of ten numbers each with an average listed at the bottom of each, say A11, B11, and C11. There are two ways you can solve this:Combine all the averages and divide by 3. [=SUM(A11:C11)/3] - But, the result may not reflect the average of the entire data set.Calbulate the average for all 30 numbers in the data set. [=SUM(A1:C10)/30] - This would give a much more accurate representation of the entire data set.


How can you average averages?

-- Multiply the first averages by the number of observation for each set of these. -- Add up the sets of averages. -- Divide the sum by the total number of observations (Add cardinaility of each set). -- The result is the average of the averages. If you say have 4 "average" value and just add these, and divide by 4, the result is "unfair" because average may be of 3 observations, while another of 1000. So, to "compensate" and make every observation just as valuable, you re-generate the "sum of sums" and then divide by the total number of observations. If all sets are the same you can divide by number of observations.


Why do we calculate averages?

That's because averages give us some idea about general tendencies.


What are some example averages from everyday life?

averages in tests, bills, income, amount of time


What is difference between variation and provisional sum?

Provisional sum is an amount quoted for an item in a tender document where all of the design information is not fully specified. The provisional sum should be as accurate as possible with the information to hand A variation is an item within a construction project that was not originally specified in the contract tender document and so is a 'variation to contract'.

Related questions

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Moving averages. And even then, they are not that good.


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How do you calculate averages on turing?

The same way you would do averages in regular math; add them all up and divide by the sum of its parts. Ex. if there's three numbers... average := (n1 + n2 + n3) / 3


How do you calculate an overall average from a set of component averages?

I recommend you do not try to average a set of components, because your result may be not be accurate. The best way to find an overall average is to average the entire data set.EXAMPLE: You have three columns of ten numbers each with an average listed at the bottom of each, say A11, B11, and C11. There are two ways you can solve this:Combine all the averages and divide by 3. [=SUM(A11:C11)/3] - But, the result may not reflect the average of the entire data set.Calbulate the average for all 30 numbers in the data set. [=SUM(A1:C10)/30] - This would give a much more accurate representation of the entire data set.


How do you get the sum and average on Microsoft Access?

You can do it through a query. If you click the SUM icon on the toolbar it will add a totals row to the design grid. Using it with any numeric fields you can get a query to do sums and averages. The totals row also gives options for other types of calculations. It is also possible to do calculated fields on forms and reports to get sums and averages.


How do you find averages in algebra?

Add all the numbers together; divide by the amount of numbers (for example, if you add three numbers, add the sum by 3).


How can you average averages?

-- Multiply the first averages by the number of observation for each set of these. -- Add up the sets of averages. -- Divide the sum by the total number of observations (Add cardinaility of each set). -- The result is the average of the averages. If you say have 4 "average" value and just add these, and divide by 4, the result is "unfair" because average may be of 3 observations, while another of 1000. So, to "compensate" and make every observation just as valuable, you re-generate the "sum of sums" and then divide by the total number of observations. If all sets are the same you can divide by number of observations.


If crc has a reliability of approximately 99.999 percent what is the reliability of checksum?

CRC is a method of checking one constant or value repeatedly to get the accurate answer(trial and error method), where as in the check sum it is not like the trial and error,since the answer got in CRC is more accurate when compared to check sum


What does a 50 percent 75 percent and a 80 percent averages out to?

This averages to be 68.33%


What is the meaning of LAM SUM?

"LAM SUM" does not have a widely recognized or standardized meaning. It could be a personal or custom term specific to a particular context or group. If you provide more context, I might be able to offer a more accurate interpretation.


Why do Indian pythons matter?

Pythons are the number one consumer of plastic bags in the world. India imports the largest sum of plastig bags globally for this reason. India averages 3 Pythons per square foot.


What is the amount of Portugal's precipitation?

With average precipitation of 4.4 inches [111 millimeters], January is the month with the most precipitation. The second highest month is March with 4.3 inches [109 millimeters]. December averages 4.1 inches [103 millimeters]. November averages 3.7 inches [93 millimeters]. February averages 2.9 inches [76 millimeters]. October averages 2.4 inches [62 millimeters]. April averages 2.1 inches [54 millimeters]. May averages 1.7 inches [44 millimeters]. September averages 1.3 inches [33 millimeters]. June averages 0.6 inches [16 millimeters]. August averages 0.2 inches [4 millimeters]. July averages 0.1 inches [3 millimeters].