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Hps2205:Quantitative Methods Question Paper
Hps2205:Quantitative Methods
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2011
QUESTION ONE (30 MARKS)
a) Define each of the following terms i. Statistics (2 Marks) ii. An index number. (2 Marks) b) Given that = {10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}; = 12,14,15,18,20,21,24; = 10,11,12,13,16,19,20,23; = 11,13,15,16,19,22,; Find; i. ( ) (2 Marks) ii. (2 Marks) c) The following represents the reported weights in kgs for 40 individuals. 47,50,79,45,46,80,82,72,75,74,57,69,65,52,55,60,64,73,61,60,71,70,68,68,65,55,50, 61,60,66,54,,70,62,53,65,66,52,72,67,58. Prepare a frequency table and state the modal class of the distribution. (4 Marks) d) The price of a bag of wheat flour has been documented with results below; Year 2002 2003 2004 2005 2006 2007 2008 Price (Kshs) 80 83 85 94 100 150 210
Construct chain base index numbers from these series. (3 Marks) e) Given 6,7,3,8,5 and 9, compute geometric mean and the harmonic mean. (2 Marks) f) Find a formula for the inverse of = 23 57 (3 Marks) g) Compute the index number for 2011 from the following data by using weighted average of price relative method. (4 Marks)
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Item Price (kshs) Quantities 2010 2011 Meat 100 115 90 Fish 120 140 80 Egg 10 12 70 Vegetable 12 18 115 Fruit 55 70 45
h) Rewrite 2 3 9 without the absolute sign. (2 Marks) i) Given the data set below;
Marks 12 13 14 16 17 18 No. of students 7 6 15 12 10 4
i. Compute the arithmetic mean. (3 Marks) ii. State the median. (1 Mark)
QUESTION TWO (20 MARKS)
a) Let U= {All students in MUCST College}; X= {Students taking an IT course} and Y= {Students taking a mathematics course}; describe the following sets in words. i. (2 Marks) ii. ( ) (2 Marks) b) The main daily newspapers in a country are; the National, The New Era and the Citizen. The management of one of the dailies was concerned about the sales volume of their papers. In a survey of 100 families conducted in the country, the numbers that read the various newspapers were found to be as follows c) Name of the newspaper No of Readers The citizen 28 The citizen and New era 8 The new era 30 Citizen and National 10 The national 42 New era and National 5 All the three papers 3
Required
i. Write the above information in a set notation. ( Marks) ii. Present the above information in the form of a venn diagram. (4 Marks) iii. How many families read at least two papers? (1 Mark) iv. How many families read the citizen or national, but not the New era? (2 Marks) v. How many families read at most two papers? (1 Mark)
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vi. How many families did not read any paper? (2 Marks) d) With some examples, distinguish between each of the following terms. i. A universal set and the compliment of a set. (2 Marks) ii. A finite and an infinite set. (2 Marks)
QUESTION THREE (20 MARKS)
a) Distinguish between unweighted and weighted index numbers. (3 Marks) b) Briefly explain any two uses of index numbers. (3 Marks) c) The prices and quantity of various commodities over two years are listed as below.
2008 2009 Item Price Quantity Price Quantity Flour 120 400 150 650 Milk 60 90 70 110 Fruit 80 100 90 130 Bread 70 120 75 180
(8 Marks) d) (4Marks) e) Briefly discuss any two limitations of index numbers. (2 Marks)
QUESTION FOUR (20 MARKS)
a) Discuss any two methods of data collection, stating one advantage and one disadvantage of each. (4 Marks) b) Distinguish between a frequency polygon and a histogram. (2 Marks) c) Given the data set below;
Marks 0-10 10-20 20-30 30-40 40-50 50-60 No. of students 7 6 15 12 10 4
Compute i. The arithmetic mean. (3 Marks) ii. The median (3 Marks) iii. The standard deviation of the distribution. (3 Marks) iv. (2 Marks) v. Represent this data in a histogram. (3 Marks)
QUESTION FIVE (20 MARKS)
a) Find the equation of a line that passes through the point (2, -5), and is perpendicular to the line 3 7 15 = 0. (3 Marks)
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b) Solve using the following simultaneous equations using the elimination method. 2 3 = 7 3 + 5 = 1 (3 Marks) c) Solve the following inequality 3 + 25 8 15. (2 Marks) d) Let the functions f and g be defined by = 2 + 1 and = 2 2. Find + 2. (3 Marks) e) Maximize = 6 + 70 subject to: i. 6 + 3 24 ii. 3 + 6 30 iii. 0; 0 (5 Marks)
f) Calculate the amount on Kshs 150,000 invested at 16% p.a for 7 years compounded quarterly. (4 Marks)
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