Question

mean: 100.7

percent error: 0.7%

standard deviation: 29.58

1. Based on the mean, percent error, and standard deviation, what can you say about your accuracy and precision? What does this say about whether your errors are primarily random or systematic? Explain your reasoning

Answer 1

Given that mean=100.7 , percent error=0.7 standard deviation=29.58

Accuracy can be generalized as closeness of a measured value to a value. which we already know For example, if in an experiment  we obtain an estimate of weight measurement of 4.5 kg for a given material, but the known weight is 10 kg, for that material then our measurement is not accurate. In this case, our measurement is not at all close enough to the true value of the material .

Precision means in layman terms as the closeness of two or more measurements of sample observations or data to each other. Using the example same as above, if we weigh a given substance five or six times, and get 4.5 kg each time, then our measurement is at good precision . Precision is independent of accuracy,we can be very precise but inaccurate, and can be less precise and accurate as the example above states my hypothesis .

so in the example given has standard deviation =29.58 , this implies that measurement is of not great precision.

percent error = [experimental value - theoretical value] / theoretical value x 100%

from above we have the idea about the percentage error

Given data has 0.7 percent error which is quite less ,this implies that measurements are close to real value.

So we have accuracy without precision.

Random errors can be defined as the statistical fluctuations in the measured data due to the precision limitations of the measurement device. Random errors usually result from the experimenter's inability to take the same measurement in exactly the same way to get exact the same number . Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations., in this case we have to take more data .  Systematic errors, are reproducible inaccuracies that are consistently in the same direction. Systematic errors are mainly due to a problem which happens  throughout the entire experiment.

the errors in above are mainly due to the random error because of the large value of standard deviation which results in more larger variance .

this is due to the inability of observer who was not able to collect the data correctly..