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# Microsoft Corporation Message Board

• hawcreek12 hawcreek12 Jan 12, 2013 5:56 PM Flag

## This needs it's own topic line: CFury insists averaging improves accuracy over sticking with significant numbers

I say there is no way for that to be consistently true with independent data points, i.e. it cannot be a rule and THAT is precisely why we even have significant digits

Here are the examples.

Average *INDEPENDENT* data points of 10.2, 10.3 10.4, 10.1, 10.4 =10.28 by CFury's assertion that is more accurate than sticking with significant digits rule.

Adhering to the rule for significant digits we are constrained to report the answer as 10.3.

Which is better? Whis is more accurate? Those numbers were read to the first decimal place only so the answer but CFury says averaging consistently increases accuracy It must be true all the time to be a rule.

Suppose the actual numbers, if they could have been read more accurately without rounding were 10.24, 10.34, 10.44, 10.08, 10.40. These round to the tenths as above but averaging the more accurate numbers we get 10.30 and one sees from above CFury's answer was actually LESS accurate IN THIS CASE, therefore there can be no rule.

If the actual numbers were all lower his answer would be closer to correct but since we cannot know that we cannot claim added accuracy.

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• [[I say there is no way for that to be consistently true with independent data points, i.e. it cannot be a rule and THAT is precisely why we even have significant digits]]

Nobody said this at all, that is why i advised you to consider the word "Likely" in the problem definition.
I have to give you a few honesty points as it does seem that you are trying.

you included two examples of a potential calculation of the results using each method.
How about picking a true value then adding random errors to create hypothetical 'measurements' then applying both methods on these noisy measurements and see which strategy creates the closer answer more often.

• **** How about picking a true value then adding random errors to create hypothetical 'measurements'

What you are proposing is scientific fraud!

The whole POINT of random averages and the law of large numbers and central limits theorem is that YOU DO NOT KNOW the "true" mean and in most cases CAN NOT KNOW the "true" mean. The whole point of your random measurements and statistical calculations is to ESTIMATE the value of the "true" mean within a range of confidence!

There are perhaps 100 billion stars in our galaxy: what is the average mass of a star in our galaxy? There is no way for sure we can know! We measure a random selection of stars in our galaxy, estimate their average mas and declare, within a certain range of confidence, that an average mass of a star in our galaxy is 5.36 solar masses. Then somebody finds a bunch of stars that are way bigger! So we re-estimate, and so on. There is no way we can ever get the "true" average.

Here you go, we produce 10,000 cases of jelly beans per day. Each case has a gross of boxes of jelly beans. On average, how many jelly beans are in each box. We want to assure our customers that there are at least 10 jelly beans in a box and not more than 13 jelly beans in a box at least 90% of the time. Remember that we are producing 10,000 new cases of jelly beans every day! We won't ever know what the "true" mean is! We must just estimate it within a range of confidence.

Here's another one: In a certain auto rating territory, within a state, we have 3375 insureds covered for collision insurance. Last year there were 1182 accidents invoking collision coverage for a total paid loss of \$2,805,645.94. What will the average loss per policy be NEXT year? You can only ESTIMATE the answer within a range of confidence! (Trust me, people using fancy statistics lose on this one every year!)

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