A chemist determined in a set of four experiments that the density of magnesium metal was 2.68g/cm3,1.69g/cm3,1.69g/cm3. The accepted value for the density is 1.74g/cm3. What can we conclude about the precision and accuracy of the chemist s data?l

let's do this 2 ways. let's assume your "chemist" measured the data exactly as written

.. 2.68

.. 1.69

.. 1.69

and let's assume that the precision in the measurement is +/- 0.01.. meaning

.. 2.68 ± 0.01

.. 1.69 ± 0.01

.. 1.69 ± 0.01

the stats..

.. mean = (2.68 + 1.69 + 1.69) / 3 = 2.02

and by formal propagation of errors (see my answer here [ Yahoo.com Link ]

couple of ways to do this.. let's do it in parts...

.. error due to sum = (2.68 + 1.69 + 1.69) ± √ [(.01)² + (0.01)² + (0.01)²] = 6.06 ± 0.02

.. error due to (6.06±0.02)/(3±0) = (6.06/3) ± (6.06/3) * √ [(.02/6.06)² + (0/3)²] = 2.02 ± 0.01

so.. our results give us a range of

.. 2,01 to 2,03

the accepted value is

.. 1.74

so our results are NOT accurate

as to precision, that's relative. +/- 0.01 is more precise that 0.1, but less precise than 0.001

.. you have to have something to compare it to.

**********

IF.. you really meant

.. 1.68

.. 1.69

.. 1.69

..

then.. the average is ..

.. 1.69 ± 0.01

again that gives us a range of 1.68 to 1.70 which does not overlap 1.74

therefore, those measurements are not accurate

and they are relatively precise.

Conclude that 2.68 g/cm3 is an anomaly.

1.69 g/c,3 is an approximate value, because of possible impurities in the sample.

As submitted , the results are neither accurate nor precise

Where is the 4th measurement?

If the 2.68 g/cm^3 is actually a typo and it should have been 1.68 g/cm^3, you can say the measurements are fairly precise as they are +/- 0.01 g/cm^3 but they aren't accurate.

Those results are neither accurate nor precise.

neither are very good. In fact poor.

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