John measured the thickness of a book using a measuring stick. He obtained the f

Question

John measured the thickness of a book using a measuring stick. He obtained the following values (in inches):

2.38; 2.36; 2.58; 2.35; 2.37; 2.40; 2.38; 2.34; 2.35; 2.41; 2.37; 23.45.

(a) Which of the given data values are probably due to either systematic error or a mistake? Why?
(b) Calculate the mean thickness of the book. Include measurements based on your answer to the question #1.
(b) Calculate the standard deviation of the mean.
(d) How do you report properly John’s experimental results for the thickness of the book? Write a sentence that explains your result.

Explanation / Answer

(a) The last measurement appears to have a large systematic error. It is several standard deviations from the mean. (b) To calculate the average, add all the numbers and divide by the total number of numbers. (b) To calculate the standard deviation of the mean: (1) Take each individual measurement and subtract the mean. This is the deviation of that measurement. (2) Square each deviation. (3) Add the squared deviations. (4) Divide by (#measurements - 1). The result of this step is the variance. (5) Take the square root of the variance. The result of this step is the standard deviation. (6) Divide the standard deviation by sqrt(#measurements). The result is the standard deviation of the mean. (d) You would report the measurement as: mean +/- standard deviation of the mean If you were to take another set of measurements, you would predict the mean (average) of the new set to fall in the range reported above.

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