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# Statistics

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1. The following list is of measured lifetimes (in thousands of hours) of a sample of a certain machine component.

5.6 4.1 6.0 5.8 5.2 4.3 6.4 5.5 6.0 5.1 4.9 4.2
4.8 6.8 5.6 5.2 7.3 5.4 4.7 5.9 5.0 6.3 4.4 6.0

(i) Group the data into classes, and draw a frequency distribution table. ( ues the classes 4.0-4.4, 4.9 etc.)
(ii) Construct a histogram and frequency polygon of the data.
(iii) Find the median, and upper and lower quartiles and use them to draw a box and whisker plot of the data.
(iv) Find the mean and standard deviation of the data.
(v) Using your frequency distribution table determine what proportion of components you would expect to last at least 5000 hours? do not assume normal distribution.

2. The following table gives the average cost per unit of an item at different levels of production.

Production Level Cost per Unit
800 30
1000 28
1200 27
1400 27
1600 26

(i) Construct a scatter plot of cost as a function of production level.
(ii) Find the equation for the linear regression equation that predicts average cost from production level.
(iii) If a production run of 1500 was planned, what is the expected average cost per unit?
(iv) Calculate the correlation co-efficient for this data and comment on it.