Download Autumn Examinations 2008/09 - Statistical Calculations and more Exams Statistics in PDF only on Docsity!
CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Autumn Examinations 2008/
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 Bachelor of Science in Computing in Information Technology support – Year 1
Programme Code: KCOMP_7_Y KCOME_6_Y KITSU_6_Y KITMN_8_Y
External Examiner(s): Dr. Brendan O’Regan Internal Examiner(s): Dr. D. O’ Connor, Ms. F. Wood
Instructions: Answer THREE questions. All questions carry equal marks.
Duration: 2 Hours
Sitting: Autumn 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) The number of people using a leisure and fitness centre was recorded each day during a 40 day period. The findings are listed below.
Daily Record: 76 143 132 122 146 128 127 119 106 113 129 116 134 101 88 151 128 131 102 158 117 131 132 130 118 121 147 121 79 112 141 97 122 150 95 133 127 124 139 124
(i) Represent the data on a stem and leaf diagram and hence form an appropriate frequency distribution having seven classes at most. Classes do not have to be equal in size.
(ii) Find the median and the first and third quartile values for the data. (12 marks)
(b) Eight candidates for a managerial post at the leisure centre were awarded marks for an interview and a psychological test. The results are as follows:
Candidate A B C D E F G H
Interview Marks 45 25 75 25 55 65 90 75
Psychological Test 35 30 55 35 65 85 70 85
Calculate Spearman’s coefficient of rank correlation and state whether it represents a measure of agreement between the two types of test. (8 marks)
- The following table shows the number of tourists (000’s) to a region per quarter for the years 2004-2007.
Quarter Year I II III IV 2004 60 80 40 14 2005 70 70 44 14 2006 70 90 44 18 2007 80 100 46 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 using the same axes as (a). (7 Marks)
(c) Find a seasonal index value for each quarter. (4 Marks)
(d) Forecast the number of tourists expected to visit the location in the third and fourth quarters of 2008. (3 Marks)
(e) Suppose the trend in the data may be depicted by the linear equation y = 54.85 + 0.12 x. [ x units : 1 quarter, x = 1 gives 1st^ quarter 2004]. Use this equation to forecast the number of tourist visits for quarters one and two of 2008. (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 = L C
N F
f M M
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
y = a + bx
Coefficient of Correlation :
2 2 2 2 2 2 2 2
. (^).
n xy x y n xy x y r n x x n y y (^) n x x n y y
∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ ∑ (^) ∑ ∑ ∑ ∑
2
−
∑ n n
d R (^) S
