Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students' results for three determinations are as follows: (1) 22.52, 22.48, 22.54 (2) 22.64, 22.58, 22.62 (b) Precision can be judged by examining the average of the deviations from the average value for that data set. (Calculate the average value for each data set; then calculate the average value of the absolute deviations of each measurement from the average.) Which set is more precise?

Video transcript

Hi everyone here we have a question telling us the percentage of calcium and a sample of water. Through a series of experiments. The following data were collected. Experiment 17.87 point 37.67 point 47.1 experiment to 7.27 point 57.67 point 47.3. And our goal is to determine which experiment is more precise. You can test the precision by calculating the average value of the absolute deviations of each measurement from the mean value. So first let's calculate the mean value. So for experiment one That would be 7. Plus 7.3 Plus 7.6 Plus 7. Plus 7.1, divided by five. And that equals 7.4. For experiment two, That would equal 7.2 Plus 7.5 Plus 7. Plus 7.4 Plus 7. divided by five, Which equals 7.4. Now we need to calculate the standard deviation. The standard deviation formula is the standard deviation equals the square root of the sun of each value from the population minus the population. Mean which we just calculated over the size of the population minus one. So for experiment one that would be 7.8 -7. Squared Plus 7.3 -7.4 Squared Plus 7.6 -7. Squared Plus 7. -7.4 Squared plus 7. -7.4 Squared. And we are going to take the square root of that over five minus one. So we get the square root of 0.3 Which equals 0.27. And now to do the same thing for experiment two. So we get the square root as 7. -7.4 sq Plus 7.5 -7. Squared Plus 7. -7.4 Squared Plus 7. -7.4 Squared Plus 7.3 -7.4 Squared over five minus one. So we get the square root of 0.0256, Which equals 0.16. And we have to remember that the smaller our standard deviation, the higher our precision and experiment to has the lower standard deviation. So experiment to is more precise and that is our final answer. Thank you for watching. Bye.