Q1 ) Imagine this: Bob the Builder is measuring the size of a room so he can buy
ID: 1487456 • Letter: Q
Question
Q1) Imagine this: Bob the Builder is measuring the size of a room so he can buy the right amount of hardwood flooring. He wants to be precise, so he does not buy too much or too little. Unfortunately, he forgot his tape measure and only has a meter stick with him. Bob uses the meter stick to measure the length of the room at the East wall to be 6.28 m. Because he has to move the meter stick along the floor several times to cover the full length of the wall, he knows there will be measuring error, so he measures it twice more, obtaining 6.30 m and 6.25 m. Thus, he has a data set with three values: {6.28 m, 6.30 m, 6.25 m}. Calculate the mean value of this data set; report the answer in meters. Q2) Calculate the standard deviation of Bob’s data set, {6.28 m, 6.30 m, 6.25 m}. Do it by hand to get a good sense of how the equation works. Then, if you know how to, you can confirm it using the statistics functions on your calculator or Excel. Q3) Bob measures the West wall of the room four times, and calculates the mean of his data set to be 6.293 m and the and standard deviation to be 0.032 m. Calculate the standard deviation of the mean (in meters) for this data set.
Q4) When you have two or more measurements in your data set (N 2), which of the following
statement(s) is/are correct?
(A) The standard deviation is always greater than or equal to zero, , (B) The standard deviation of the mean is always greater than or equal to zero, , (C) The standard deviation is always larger than or equal to the standard deviation of the mean, , (D) Answers A and B, (E) All of answers A, B, and C.
Explanation / Answer
Q1)
Mean is average of all three values, 6.2766 m.
Q2)
Standard deviation is calculated as follows
sqrt( (6.2766-6.28)^2+(6.2766-6.30)^2+(6.2766-6.28)^2)/3) = 0.0137
Q4)
The standard deviation will always be at least as large as the mean absolute deviation.
So, E is correct
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