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CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 1 Examinations 2007/
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 Higher Certificate in Science in Computing in Information Technology Support
Programme Code: KCOMP_7_Y KCOME_6_Y KITSU_6_Y
External Examiner(s): Dr. P. Robinson Internal Examiner(s): Ms. J. English, Mr. K. Kelly, Ms. F. Wood
Instructions: Answer THREE questions. All questions carry equal marks.
Duration: 2 HOURS
Sitting: Winter 2007
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the correct examination paper. If in doubt please contact an Invigilator.
1.(a) The data below shows the average weekly mileage travelled by sales representatives working for a large company:
Mileage: 342 436 729 294 332 274 421 379 470 255 517 376 285 478 259 680 838 295 396 615 385 311 772 550 447 325 593 302 101 241 468 433 586 315 115
(i) Represent the data on a stem and leaf diagram. Hence form a frequency distribution with six classes at most. Classes do not have to be of equal interval. Comment on the shape of the distribution.
(ii) Determine the median and quartile values for the data. (12 marks)
(b) Nine employees working for the company were chosen at random and their ages and salaries were noted. The details are as follows:
Employee A B C D E F G H I
Age last birthday 32 39 45 26 37 50 45 35 42
Salary (€000’s) 54 33 36 51 84 45 39 69 33
Calculate Spearman’s coefficient of rank correlation and comment on the relationship between age and level of salary. (8 marks)
2.(a) The following table shows the prices obtained for houses sold in a given area by a certain auctioneering firm during the year 2007:
Price (€000’s) No. of Houses 100 but less than 200 4 200 but less than 300 15 300 but less than 350 32 350 but less than 400 18 400 but less than 500 5 500 but less than 600 2 600 but less than 800 4
(i) Calculate the mean house price ( x ) and the standard deviation ( s ) from the mean. (ii) Represent this data on a histogram. (iii) Find the median of the distribution and calculate a coefficient of skewness for the data.
(16 marks)
(b) Describe some methods of collecting data, listing the advantages and disadvantages of same. (4 marks)
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
Alternative formulae :
x f x x or x n f
= ∑^ =∑
Mode = XL
L
W
L R
∆^ + ∆
( )
n
n
x x
n
x x SD
2 2 ( )^2
( )
2 fx^2^ fx f SD f
∑ ∑ ∑ ∑
x x MAD n
∑^ −
Pearson =
3(Mean - Median) Standard Deviation
QCS =^3 2 2
3 1
( Q Q ) ( Q Q )
Q Q
( )( )
( )
2 2
x y xy b n x x n
∑ ∑ ∑
∑ ∑
a = y − bx
( )( )
( ) ( )
2 2 2 2
x y xy R n x y x y n n
∑ ∑ ∑
∑ ∑ ∑ ∑
Alternative formulae :
x f x x or x n f
= ∑^ =∑
Mode = XL
L
W
L R
∆^ + ∆
( )
n
n
x x
n
x x SD
2 2 ( )^2
( )
2 fx^2^ fx f SD f
∑ ∑ ∑ ∑
