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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2009/
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): James Reilly Internal Examiner(s): Dr. D.O’Connor, Ms. F. Wood
Instructions: Answer THREE questions. All questions carry equal marks.
Duration: 2 HOURS
Sitting: Winter 2009
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) Mathematical Software packages are constantly being improved. The following table shows the times taken for each of 45 sophisticated calculations to be carried out using given software.
Time Taken (secs): 3.4 4.5 3.5 4.1 1.9 4.1 3.0 5.6 2. 2.3 8.7 4.1 5.2 3.2 2.6 8.6 6.0 6. 7.1 4.5 2.0 3.8 2.7 3.2 2.8 3.5 9. 4.9 6.3 3.4 3.7 1.6 6.4 3.1 5.7 4.
(i) Arrange the data in a stem and leaf diagram and hence form a frequency distribution having at most seven classes. Classes do not have to be equal in size.
(ii) Find the median and the first quartile values for the data. (12 marks)
(b) The table below gives the annual salary (€000’s) and the age of a sample of employees working for a software development company:
Salary 48 37 39 51 58 64 58 57
Age 29 45 29 47 51 37 33 58
Calculate Spearman’s coefficient of rank correlation and comment on the relationship between age of employee and the salary earned. (8 marks)
- ‘COMPURENT’ is a hire company for computers, photocopiers and office equipment. A survey of 100 small companies was carried out to determine their cost of rentals. The quarterly rental costs are presented in the table below:
Quarterly Rental(€00’s) No. of Companies
10 but less than 25 13 25 but less than 40 9 40 but less than 50 24 50 but less than 60 31 60 but less than 70 18 70 but less than 90 5
- The following table shows the number of new visitors per quarter to a website per quarter for the years 2005-2008.
Quarter Year I II III IV 2005 30 50 80 10 2006 40 40 90 10 2007 40 40 90 20 2008 50 30 100 20
(a) Plot a graph of the time series. (4 Marks)
(b) Use a 4-quarter centered moving average to calculate a trend for the data. Plot the trend the same axes as (a). (7 Marks)
(c) Find a seasonal index value for each quarter. (4 Marks)
(d) Forecast the number of visitors expected to visit the location in the second and third quarters of 2009. (3 Marks)
(e) Suppose the trend in the data may be depicted by the linear equation y = 42.5 + 0.4412 x. [ x units : 1 quarter, x = 1 gives 1st^ quarter 2005]. Use this equation to forecast the number of tourist visits for last two quarters of 2009. (2 Marks)
Statistical Formulae
Descriptive Statistics
Mean :
x
fx f
Standard Deviation :
f ( x x )^2 s f
∑^ −
2 2 fx fx s f f
∑ ^ ∑
Median =
1 2 M 1 M M M
N F
L C
f
+ ^ −^ −
Mode =
1 (^21 )
M M M M M M M
f f L C f f f
− − +
−^ +
Regression and Correlation:
y ' = a + bx a
y b x n
∑^ y^ =^ na^ +^ b^ ∑ x
b
n xy x n x x
y
∑ ∑ ∑ ∑ 2 ∑^2
∑^ xy^ =^ a^ ∑ x^ +^ b^ ∑ x^2 y^ =^ a^ + bx
Coefficient of Correlation :
r
n xy x n x x n y y
y
∑ ∑ ∑ ∑ 2 ∑^2. ∑^2 ∑^2
( (^ ) ) ( (^ ))
2 2 2 2 .
n xy x y
n x x n y y
∑ ∑ ∑
∑ ∑ ∑ ∑
Spearman’s Coefficient of Rank Correlation : ( 1 )
2
−
∑ n n
d R (^) S
Coefficient of Variation: 100 s x
×
