Question 8.98

image 67. Antonio measures the alcohol content of whiskey for his Chemistry 101 lab. He actually measures the mass of 5 milliliters (ml) of whiskey—a chemical calculation—and then finds the percentage of alcohol from the mass. The standard deviation of students’ measurements of mass is milligrams (mg). Antonio repeats the measurement three times and records the mean of his three measurements.

  1. What is the standard deviation of Antonio’s mean result?
  2. How many times must Antonio repeat the measurement to reduce the standard deviation of to 5 mg? Explain to someone who knows nothing about statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.

67.

(a) The standard deviation of the average measurement is

(b) To cut the standard deviation in half (from 10 mg to 5 mg), we need measurements because is then . Averages of several measurements are less variable than individual measurements, so an average is more likely to give about the same result each time.