Question 192153: Q2) Give a data set we can calculate the sample mean,the sample median and the sample variance.
a] Giving a reason, state whether each of the following is true or false
(i) The sample mean is always greater than zero
(ii) The sample mean is always smaller than the sample median
(iii) The sample variance is a better measure of location than the sample median
(iv) Two numbers in a data set can be changed without altering the sample median
b] The following is a sample of Rio De Janeiro commuter's travel times
10, 30, 5, 25, 40, 20, 10, 15, 30, 20, 15, 20, 85, 15, 65, 15, 60, 60, 40, 45 (in mins)
Calculate:
(i) the sample mean
(ii) the sample median
(iii) the sample variance
Estimate the probability that a randomly chosen commuter's travel time lies between 37.5 minutes and 62.5 minutes.
Plot the data and state, giving reasons, whether you think that the underlying distribution is normal
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Q2) Give a data set we can calculate the sample mean,the sample median and the sample variance.
a] Giving a reason, state whether each of the following is true or false
(i) The sample mean is always greater than zero
Ans: false ; the data set may only contain zeroes
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(ii) The sample mean is always smaller than the sample median
Ans: false
Consider the set 1,2,1000
median = 2 ; mean = 1003/3 = 334.3333
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(iii) The sample variance is a better measure of location than the sample median
Ans: false ; variance is a measure of spread
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(iv) Two numbers in a data set can be changed without altering the sample median
Ans: false ; not if their value is changed
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b] The following is a sample of Rio De Janeiro commuter's travel times
10, 30, 5, 25, 40, 20, 10, 15, 30, 20, 15, 20, 85, 15, 65, 15, 60, 60, 40, 45 (in mins)
Comment: This is arithmetic. I'll let you do that.
Cheers,
Stan H.
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Calculate using your calculator:
(i) the sample mean
(ii) the sample median
(iii) the sample variance
Estimate the probability that a randomly chosen commuter's travel time lies between 37.5 minutes and 62.5 minutes.
Plot the data and state, giving reasons, whether you think that the underlying distribution is normal
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