Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The standard deviation of students' lab measurements is σ = 11.3 milligrams. Juan repeats the measurement 6 times and records the mean x of his 6 measurements.
(a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making 6 measurements and averaging them, what would be the standard deviation of all his x's?)
mg.
(b) How many times must Juan repeat the measurement to reduce the standard deviation of x to 3.2 milligrams?
Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.
The average of several measurements will always have a greater standard deviation than the result of a single measurement.
The average of several measurements will always equal the true mean.
The average of several measurements is much more likely to be close to the true mean than a single measurement.