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Ogive - Quantitative Analysis - Exam, Exams of Quantitative Techniques

Jaypee University of Engineering & TechnologyQuantitative Techniques

Main points of this past exam are: Ogive, Responses, Businesses, Spent, Third Quartile, Histogram, Ogive, Frequency Distribution, Distribution Table, Equal Size

Typology: Exams

2012/2013

Uploaded on 03/28/2013

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Cork Institute of Technology
Higher Certificate in Science in Computing (ACCS) – Stage 1
(NFQ – Level 6)
Autumn 2006
Quantitative Analysis
(Time: 3 Hours)
Answer FIVE Questions.
All questions carry equal marks.
Examiners:
Dr S. O Rourke
Ms M. Meagher
1. A number of businesses were asked how much money they spent each year on rub-
bish disposal. Their responses are summarised as follows (all figures are given in
thousands of euros).
1.32 2.31 2.13 2.91 2.17 1.39
1.67 2.09 1.36 1.87 1.77 2.19
2.20 1.81 2.08 2.00 2.28 1.48
1.51 2.20 2.18 2.85 1.79 1.65
2.01 1.30 2.64 1.58 2.02 1.41
(a) Form a frequency distribution table with 8 class intervals of equal size.
(6 marks)
(b) Draw a histogram for the data. (4 marks)
(c) Draw an ogive for the data. (4 marks)
(d) Use the ogive to estimate the median, and the third quartile and the third decile
of the data. (6 marks)
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Cork Institute of Technology

Higher Certificate in Science in Computing (ACCS) – Stage 1

(NFQ – Level 6)

Autumn 2006

Quantitative Analysis

(Time: 3 Hours)

Answer FIVE Questions. All questions carry equal marks.

Examiners: Dr S. O Rourke Ms M. Meagher

  1. A number of businesses were asked how much money they spent each year on rub- bish disposal. Their responses are summarised as follows (all figures are given in thousands of euros).

(a) Form a frequency distribution table with 8 class intervals of equal size. (6 marks) (b) Draw a histogram for the data. (4 marks) (c) Draw an ogive for the data. (4 marks) (d) Use the ogive to estimate the median, and the third quartile and the third decile of the data. (6 marks)

  1. The following data gives the average number of minutes per day spent by a sample of 200 people on the internet.

0 but less than 20 17 20 but less than 40 28 40 but less than 60 45 60 but less than 90 37 90 but less than 120 32 120 but less than 150 21 150 but less than 180 11 180 but less than 240 9

(a) Calculate the mean and the standard deviation of the data. (8 marks) (b) Calculate the median of the data. (6 marks) (c) Calculate the coefficient of skewness of the data. Comment on your findings. (6 marks)

  1. (a) A manufacturer of electrical components finds that 95% of parts produced on a particular line pass all quality control tests. Twelve parts are chosen at random. Assuming a binomial distribution, find the probability that (i) all 12 parts will pass all quality control tests. (ii) at least three parts will not pass all tests. (6 marks) (b) The number of staff arriving at the factory each minute between 8.45 and 9. is found to follow a Poisson distribution with a mean of one person per minute. Find the probability that between 8.45 and 9. (i) exactly 30 staff arrive. (ii) fewer than five staff arrive. (7 marks) (c) The mean diameter of the part produced by a particular machine is 6mm with a standard deviation of 0. 3 mm. Assuming a normal distribution, find the probability that a randomly chosen part has diameter (i) greater than 6. 3 mm. (ii) between 5. 8 mm and 6. 1 mm. (7 marks)
  1. (a) What is a tautology? When are two propositions said to be logically equivalent?

Draw the truth tables for the following compound propositions. (i) p ⇒ (p ∧ ¬q) (ii) p ∧ (p ⇒ q) (iii) ¬p ∨ ¬q (10 marks) (b) In a group of 200 people in a casino, 46 people play roulette and nothing else, 41 play blackjack and nothing else, and 32 play poker and nothing else. Moreover, 11 people play both blackjack and roulette, 9 people play roulette and poker, 9 people play both blackjack and poker, while 66 people play none of these. (i) Represent the data on a Venn diagram. (ii) How many people play all three games? (iii) How many people play poker and roulette but not blackjack? (iv) How many people play only two of these games? (10 marks)

  1. (a) A manufacturer of matches claims that the average contents of a box of matches is 40 with a standard deviation of 2. A random sample of 100 boxes of matches is found to contain an average of 39.5 matches. Can the manufacturer’s claim be maintained at the 95% level of confidence? At the 99^34 % level of confidence? (10 marks) (b) Consider the function f (x) = 21 + 4x − x^2.

(i) Calculate the derivative f ′. (ii) Find all critical points of the function f. (iii) Hence find the points where f has a local maximum or local minimum. (10 marks)