Do the following measurements have a good precision but a poor accuracy, or a good accuracy but a poor precision? Why?
(a) You have weighed a beaker 6 times and got the following data: 40.2250g, 40.2245g, 40.2242g, 40.2253g, 40.2258g, and 40.2249g. However, you realized you had forgotten to tare the balance before your measurements.
(b) One group of students is asked to measure the length of a piece of paper by using a centimeter long ruler and report their data as: 11.5cm, 9.0cm, 12.0cm, 10.0cm, 7.0cm, 13.0cm, 8.0cm, 11.0cm, and 8.5cm. And you know the length of the paper is 10.0 cm.
(c) You have made 8 measurements of the calcium concentration in an unknown solution, corrected to a calcite standard. The data are: 10.01%, 10.02%, 10.03%, 10.00%, 9.99%, 10.00%, 9.98%, and 10.01%. Unfortunately, you were informed that due to temperature variation, the calcium concentration of the standard has a 5% offset.
Precision is the measure of variation(difference) among the repeated experiments. Less the range, higher the precision or vise-versa.
Precision can be calculated by arranging the values in ascending order to identify the lowest and highest value. Then calculating the range by taking difference of highest and lowest values.
Accuracy means the closeness of observed values with the true value. Accuracy can be calculated by comparing the mean(average) with true value. Mean value closer to the true value shows good accuracy or
(a) Weight of the beaker are recorded without taring. It indicated there may be difference in the true value and the observed value, so we can say poor accuracy
Average can be calculated as
( 40.2242 + 40.2245 + 40.2249 + 40.2250 + 40.2253 + 40.2258 ) / 6 = 241.3497/6 = 40.22495
The observed values are almost closer (less difference between the individual observation or measurements) indicated good precision
Range can be calculated as 40.2258 - 40.2242 = 0.0016
Answer: Good precision but a poor accuracy
(b) We have the true value that is 10cm
Average (mean) of the 9 observations is
(7.0+8.0+8.5+9.0+10.0+11.0+11.5+12.0+13.0) /9 = 90.0/9 = 10.0
Which is exactly a true value indicating the good accuracy
The variation (difference) between observation is more. Range is 13.0-7.0 = 6.0
Too much variation can be said as poor precision
Answer : Poor precision but a good accuracy
(c) The calcium concentration of standard has 5% of offset indicates the difference between observed values and the true value shows poor accuracy
Average can be calculated as
(9.98 + 9.99 + 10.00 + 10.00 + 10.01 + 10.01 + 10.02 + 10.03 )/8= 10.04/8 = 10.005
Closeness of the observed values indicates the good precision
Range is 10.03-9.98=0.05
Answer : Good precision but a poor accuracy
Do the following measurements have a good precision but a poor accuracy, or a good accuracy...