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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2010/
Module Title: Statistical Calculations
Module Code: STAT 6006
School: School of Computing & Mathematics
Programme Title: Bachelor of Science in Computing – Year 1 Higher Certificate in Science in Computing – Year 1
Programme Code: KCOMP_7_Y KCOME_6_Y KITSU_6_Y KITMN_8_Y
External Examiner(s): Mr. James Reilly Internal Examiner(s): Ms. C. Palmer, Dr. D.O’Connor, Ms. F. Wood
Instructions: Answer THREE questions. All questions carry equal marks.
Duration: 2 HOURS
Sitting: Autumn 2011
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you are attempting the correct examination. If in doubt please contact an Invigilator.
1.(a) The time spent (in seconds) by a group of employees performing a task was recorded as follows:
7.2 2.7 5.7 4.8 7.5 7.0 1.0 7. 1.5 6.9 4.3 1.5 4.4 4.6 6.4 1. 4.2 6.5 2.9 8.6 5.1 5.0 1.8 4. 7.3 1.5 2.5 8.9 3.3 5.6 6.3 7. 6.3 8.4 3.5 6.4 3.6 5.8 5.2 6.
(i) Arrange the data in a stem and leaf diagram and use this diagram to find the inter quartile range (IQR).
(ii) Form a frequency distribution with six classes. Classes do not have to be equal in size.
(12 marks)
(b) In a factory the mean annual wage for male employees was calculated as €32, per year with a standard deviation of €1,542. Female employees were found to have a mean annual wage of €33,950 with a standard deviation of €1,628. Which group of employees has the greater variability in wages? Justify your answer.
(4 marks)
(c) Briefly explain the following:
(i) standard deviation
(ii) third decile.
(4 marks)
- Researchers at the European Centre for Road Safety Testing are trying to find out how the age of cars affects their braking capability. They test a group of eight cars of differing ages and find out the minimum stopping distances that the cars can achieve. The results are set out in the table below:
Age of Car Minimum Stopping Distance (months) x at 40kph: (metres) y
(a) Represent the data on a scatter diagram. (4 marks)
(b) Use the method of least squares to find the regression line of y on x and plot this line on the scatter diagram in part (a). (10 marks)
(c) Calculate the coefficient of correlation and interpret your answer. (4 marks)
(d) If a car is 90 months old, what stopping distance would you expect? How reliable do you think this prediction would be?
(2 marks)
- The table below shows quarterly passenger numbers using a national ferry service during the years 2007 to 2010 inclusive.
Figures (000s)
YEAR QUARTER
I II III IV
2007 52 74 91 53 2008 49 62 79 50 2009 38 49 63 45 2010 47 68 74 51
(a) Plot the data on a time series graph. (4 marks)
(b) Calculate a four quarter centred moving average for the data and plot this on your graph in (a).
(9 marks)
(c) Use a multiplicative model to determine seasonal index values for the data.
(5 marks)
(d) The trend in the data can be depicted by the linear equation y 64.7 0.66 x [ x units: 1 quarter, x = 1 gives 1st^ quarter 2007] Use the linear trend equation and the seasonal index to forecast passenger figures for the first two quarters of 2011.
(2 marks)
