A Problem from a Chem Workbook

[cafegurl]

I've been studying up for my GED exam and to get ready for college. So I bought the Chemistry Workbook for Dummies. There is a question that i am unsure of how to go about on it.. If any of you would like to show the steps in how to solve this type of problem i would love it..

 

 

Ok, so here it is...

 

"Two Jewelers were asked to measure the mass of a gold nugget. The true mass of the nugget was 0.856 grams. Each jeweler took three measurements. The average of the tree measurements was reported as the "official" measurement with the following results.

 

Jeweler A: 0.863 g, 0.869 g, 0.859 g.

Jeweler B: 0.875 g, 0.834 g, 0.858 g

 

Which Jeweler's official measurement was more accurate? Which jeweler's measurements were more precise? In each case what was the error and percent error in the official measurement? "

 

So you all know i am a total newbie to Chemistry and this question is on page 15... Any ideas?..

[MM6]

Precision and accuracy are not concepts dedicated solely to chemistry, they apply to every application of measurement.

 

Something (e.g., measuring device) is accurate if it reports the actual measure of something.

 

Something is precise if it reports the same (within some given range of error) measurement on multiple trials.

 

Can you get the answer using these definitions? You should! You must use your own smarts! If you wager an answer, I'll verify it.

 

The formula for percent error is % error = | experimental result - accepted value | / accepted value x 100 %

 

Find the average of each jeweler's results (add the three values and divide by three). In the percent error equation this will be the "experimental result".

Edited April 19, 2009 by MM6

[cafegurl]

Ok so when i take and do what you say i get:

 

Jeweler A: 0.863g = 0.7 , 0.869g = 1.3, 0.859g = 0.3

These decimals divided by 3 = 2.6

 

The Percentages are: 99.1%, 98.5%, 99.6% and divided by 3 = 230.8

I also, got an average of 99% for jeweler A...

 

 

Jeweler B: 0.875g =1.9, 0.834g = -2.2, 0.858g = 0.2

These decimals divided by three = 4.3

 

The Percentages i got were: 97.8%, 102.6%, 99.7% = 233.6

I also, got an average of 100% for jeweler B.

 

So i think that Jeweler A is more Accurate and Jeweler B is more Precise...

 

i went out of my way spit balling any and every possibly answer... is there an easier way?

[MM6]

Cafegirl,

 

It looks like your mistake was in how you computed and used the average.

 

Here is my solution:

 

 

Jeweler A official measurement (average of the 3) = 2.59/3 = 0.867

 

Jeweler B official measurement (average of the 3) = 2.57/3 = 0.856

 

 

 

So....

 

Jeweler B has the more accurate measure (it's matches the true mass of the nugget)

 

However,

 

Jeweler A has the more precise measurement. Even though his average is less accurate, his measurements are more similar to one another than that of Jeweler B.

 

 

Jeweler A % error = = | 0.867 - 0.856 | / 0.856 x 100 % = 1.29%

 

Jeweler B % error = 0

[cafegurl]

The only part i'm not understanding is how you got the 2.59 and 2.57 i can't seem to recreate that... Other than that i understand this perfectly. Thanks for the help..

[iNow]

To get the average, you must add each individual measurement together, then divide by the number of measurements.

 

 

Jeweler A: 0.863 g + 0.869 g + 0.859 g = 2.591

Jeweler B: 0.875 g + 0.834 g + 0.858 g = 2.567

 

 

Divide each by 3 (since that's the number of measurements you added together in your average).

 

Jeweler A avg = 2.591/3 = 0.8637

Jeweler B avg = 2.567/3 = 0.8557

[cafegurl]

Ok, thankyou! I get it now! :-D