Principles of Statistics-exams

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K AMPALA INTERNATIONAL UNIVERSITY

FACULTY OF SCHOOL OF COMPUTER STUDIES

UNIVERSITY EXAMINATIONS 2011

COURSE : BCS, BCI, BBC, BIT

PAPER : Introduction to principles of Statistics

CODE : CS1202

YEAR : I

SEMESTER : I

DATE : 31ST May 2011

TIME : 2-5PM

DURATION : 3Hrs

Instructions

Attempt ALL Questions in SectionA and ANY Three from section B

r2= 1- 6 D 2 =a+ bX b= (X- X)(Y- Y)n(n2- 1) (X- ) 2

SECTION A COMPULSORY QUESTIONQuestion. 1

a) Briefly write down the meaning of the following

(i) Sample

(ii) Population


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(iii) Statistics

(iv) Parameter (3 Marks @)

b) Define a data source. [3 mark]

ii) Give the meaning of both primary and secondary data, give examples in each case.

[6 marks]

c) Give the difference between the following

i) Statistical inquiry and sampling [3 marks]

ii) Give two advantages and two disadvantages of sampling [4 marks]

iii) State what you understand by simple random sampling, stratified sampling, cluster sampling and

judgmental sampling [ 8 marks]

iv) Population and a Sample [4 marks]

d) Differentiate between homogeneous and heterogeneous populations [2 marks]

SECTION B, Attempt ONLY Three Questions

Question2

a) Give two reasons why sampling should be used [ 5 marks]

b) What is sampling distribution [3 marks]

c) The following is a table of grouped data for the days of maturity for 40short term investmentsfound in national business and financial weekly paper.

Day to matching frequency

30-40 3

40-50 1

50-60 8

60-70 10

70-80 7

80-90 7

90-100 4

a) Use the sample to estimate


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(i) Sample mean

(ii) Mode

(iii) Inter quartile range

b) Draw an o-give and use it to estimate the median

Question3

The data below shows the ages of people in the central region of Uganda who didnt activelyparticipate in CHOGM preparations of 2007.

47 73 65 66 72 75 55 45 71

72 60 64 53 69 60 83 68 65

79 61 52 55 70 62 57 56 80

68 70 50 61 62 52 54 58 50

74 59 46 70 70 67 74 63 55

a) Determine the following:

i) State the variable under investigation [1 mark]

ii) The Range [1 mark]

iii) Class width [2 marks]

b) Construct a frequency distribution table for the data. [12 marks]

c) Calculate the Arithmetic Mean Age [4 marks]

Question. 4

The following are data collected from Gongo la mboto shops showing the categorical profitrealization ($) in the month of August 2009.

Profit per Shop ($) 0 9 10 19 20 29 30 39 40 49 50 - 59

No. of Shops 12 18 27 20 17 6

a) Represent the information a frequency table and show the cumulative frequency.

[8marks]


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b) Draw both the less than and greater that Ogive [7 marks]c) Using both the formula and graphical methods, calculate the median. Comment on the

two, and give the difference that exists if any. [5 marks]

Question. 5

The table below shows the frequency distribution of the persons employed in units of Azamindustries in Tanzania. If the frequency of the first class interval is 6, study the table and answerthe following questions.

Calculate

i) The average number of persons employed. [ 8 marks]ii) The mode [ 5 marks]

iii) Draw for the frequency polygon for the employees [ 7 marks]

Question. 6

Using the formulae: r2= 1- 6 D2

n(n2- 1)Calculate the Spearman correlation coefficient r2 between anxiety and performance of

biology test. (15 marks)

Student 1 2 3 4 5 6 7 8

Anxiety Score 25 28 31 31 35 42 45 49

Biology Score 17 16 15 15 13 15 15 10

Class

Interval

Less than Cumulativefrequency

5 - 9 6

10 14 11

15 19 26

20 24 36

25 29 41

30- 34 45

35 39 47

40- 44 50


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Question. 7

A statistics teacher administers a test to a group of 100 students and

obtainsthe following results.

Score 1 2 4 5 7 8 9 10 13 14 16 17 18

Frequen

cy

5 8 10 10 3 4 12 15 20 8 2 2 1

a) Construct a grouped frequency using 3 as class size.

b) Use (a) to determine the relative frequency distribution of the data

c) Use (a) to plot the ogive of the data. (15

marks)

Question. 8

The number of hours spent studying should be related to performance in an

examination. To verify this assertion, a teacher registers the number of hours

(per week) six students spend studying physics and the marks they obtain in

the physics examination as follows:

Student 1 2 3 4 5 6

Time

studying

8 7 15 4 11 14

Exams

score

13 10 16 12 13 17

a) Draw a scatter diagram of the data

b) Use the scatter diagram to estimate the line of best fit

c) Use the method of least squares to determine the line of best fit.


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d) Compare the lines in (b) and (c) above.

e) What would be the estimated score for a student who spends 10 hours

a week studying? (15 marks)

Question. 9

(i)What is measurement? (3 marks)

(ii) Using examples explain the different measurement scales used

statistical data

Analysis (12

marks)

Question. 10

The following probability of each outcome is given below

Colour Yellow Blue Green Violet Black

Probability 0.3 0.1 0.2 0.1 0.3

Calculate the probability that a lecturer at KIU will

a) Wear a blue or violet tie

b) Wear a green or blue or black suit

c) Would wear green and yellow tie

d) Will not wear a black or green or yellow shirt. (15 marks)

END

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Principles of Statistics-exams