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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2007/
Module Title: Statistical Calculations
Module Code: STAT 6006
School: School of Computing & Matematics
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
External Examiner(s): Dr. P. Robinson Internal Examiner(s): Mr. Kevin Kelly, Ms. J. English, Ms. F. Wood
Instructions: Answer THREE questions. All questions carry equal marks.
Duration: 2 HOURS
Sitting: Autumn 2008
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) An accountant, working from home, wishes to determine the average duration of business telephone calls. Over a period of time, forty telephone calls were monitored and the duration of each call is listed below.
Duration (minutes): 6.1 4.9 3.2 3.6 10.3 8.7 14.3 6. 7.4 8.3 4.1 11.2 3.7 5.3 5.7 4. 5.3 9.2 7.2 5.1 8.4 6.5 5.2 3. 4.6 5.8 5.9 12.4 9.4 4.3 12.7 4. 4.2 7.7 4.4 11.5 7.5 6.2 11.8 6.
(i) Represent the data on a stem-and-leaf diagram. Summarise your findings in a frequency distribution having eight classes at most. Classes do not have to be of equal interval.
(ii) Determine the median and the first quartile for the data.
(iii) What percentage of telephone calls is of more than 8 minutes duration? (12 marks)
(b) The accountant is considering renting office space in his local town. The table below shows the monthly rents and square footage of seven office rentals:
Office A B C D E F G
Square Footage 350 400 400 480 500 550 700
Monthly Rent (€) 860 1280 920 1060 1420 1280 1350
Calculate Spearman’s coefficient of rank correlation and comment on the relationship between size of office and monthly rent. (8 marks)
- The table below shows the number of cars rented by a car rental company for the years 2005 to 2007. The figures are recorded on a quarterly basis.
YEAR QUARTER
I II III IV
2005 642 1,020 1,410 825 2006 791 1,260 1,725 1, 2007 902 1,562 2,005 1,
(i) Plot the data on a time series graph. (4 marks) (ii) Calculate a four quarter centered moving average for the data and plot this on your graph in (i) (7 marks) (iii) Using a multiplicative model, determine seasonal index values for the data. (5 marks) (iv) The trend in the data can be depicted by the linear equation y = 881. 3 + 43. 4 x [ x units : 1 quarter , x = 1 gives 1st^ quarter 2005] Use the linear trend equation and the seasonal index to forecast figures for the four quarters of 2008. (3 marks) (v) Comment on the trend for 2008. How does it compare with the trend in previous years? (1 mark)
Statistical Formulae
Descriptive Statistics
Mean :
x
fx f
∑
∑
f
c f d x a c
.
Standard Deviation :
f
f ( x x )^2
2 2
∑
∑ − ∑
∑
f
c fd
f
c fd
σ c
or
2 2
f
fx f
fx
Median =^ L C
N F
M M f
M M
1 2 1
Mode =
L C
f f M M f f f
M M M M M
− +
1 (^21 )
Regression and Correlation y ' = a + bx
∑^ y^ =^ na^ +^ b^ ∑ x
∑^ xy^ =^ a^ ∑ x^ +^ b^ ∑ x^2
a
y b x n
b
n xy x n x x
y
∑ ∑ ∑ ∑ 2 ∑^2
a
y x x xy n x x
∑ ∑ ∑ ∑ ∑ ∑
2 2 2 y^ =^ a^ + bx
Coefficient of Correlation :
r
n xy x n x x n y y
y
∑ ∑ ∑ ∑ 2 ∑^2 ∑^2 ∑
2
. (^1 )
2
−
∑ n n
d R (^) S
