Juan makes a measurement in a chemistry laboratory and records the result in his
ID: 3181502 • Letter: J
Question
Juan makes a measurement in a chemistry laboratory and records the result in his lab report. Suppose that if Juan makes this measurement repeatedly, the standard deviation of his measurements will be sigma = 10 milligrams. Juan repeats the measurement four times and records the mean x bar of his four measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making four measurements and averaging them, what would be the standard deviation of all his values?) (b) How many times must Juan repeat the measurement to reduce the Standard deviation of x bar to 2? Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.Explanation / Answer
15.10 Solution:
a) Standard deviation of all his x = 10/4 = 5
b) Assume he has to repeat the meaurement n times to reduce it to 2
10 / n = 2
n = 5
n= 25
He has to measure 25 times to reduce the standard deviation of x to 2.
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