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### Topic: Most accurate measurement  (Read 376 times)

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#### packageoffat

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##### Most accurate measurement
« on: September 01, 2019, 10:57:55 PM »
Hello,

So for a problem there are 5 groups of 5 students each, and each group was given a metal rod of approximately 10 cm long to measure. Then all the measurements of each student are provided (each row is a group):

10.1 10.4 9.6 9.9 10.8
10.335 10.527 10.201 10.011 10.155
12.14 12.17 12.15 12.14 12.18
10.05 10.82 8.01 11.5 10.78
10 11 10 10 10

We are then asked which group had the most accurate measurements and which group had the most precise measurements. So for precision I know to calculate standard deviation and choose the group with the smallest but for accuracy I am confused on whether sig figs matter, or if accuracy is evaluated on how close each individual measurement is to 10 or how close the average is to 10. Would appreciate any help.

#### Vidya

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##### Re: Most accurate measurement
« Reply #1 on: September 02, 2019, 01:16:51 AM »
Which is more accurate ?
For that you must have true value and then you can compare of average with true value .
Accurate are precise also -- you can see two groups of data very precise but all precise are not accurate .

#### jeffmoonchop

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##### Re: Most accurate measurement
« Reply #2 on: September 02, 2019, 11:54:23 PM »
Some analytical methods are written as, 'accurately weigh approximately 10g'. It means that you should weigh around 10g but do it to 4 or 5dp. The method might not need it to be exactly 10g if the calculation corrects for it.

Precision means that you are weighing the same value 6 times in a row (or multiple times). You can be precise by weighing 10.4000g 6 times, but it's not accurate. To be accurate you need to weigh 10.0000g. To be accurate and precise you need to weigh 10.0000g grams 6 times in a row.

#### Fudjsk

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##### Re: Most accurate measurement
« Reply #3 on: September 21, 2019, 10:18:44 PM »
You always use the smallest number of significant figures used like 1.23423*1.0 should equal with proper significant figures, 1.2.
You could say accuracy and precise is a dartboard. If you throw 5 darts and they all hit the bullseye. Then they are precise and accurate. Usually, this is what we aim for in any science. If you threw 5 darts and they all hit the same spot but not the bullseye than they are precise but not accurate. If you throw five and neither of them land in the same spot or land on the bullseye than they are neither precise nor accurate. You can translate this to math with the bullseye being the desired outcome.