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1 National College of Ireland Higher Certificate in Business Full-time Year 1 HCBS 1 Autumn / Repeat Examinations 2015/2016 Thursday 18 th August pm 4.00pm Quantitative Analysis 1 Ms Patricia Doherty Ms Michelle Ahern Duration of exam: Attachments: 2 hours Formula Sheet (at end of exam paper) Answer any three questions. All questions carry equal marks You should answer only the required number of questions. If you answer more than the required number of questions you should cancel (put a line through) the question(s) you do not want marked. If you do not cancel extra questions, the examiner will mark the questions in the order presented in your answer book until the required number of questions have been marked. NON PROGRAMMABLE CALCULATORS MAY BE USED IN THIS EXAMINATION Page 1 of 5

2 Question 1 (50 marks) A sample of NCI students who own a PlayStation 4 were asked what were their favourite games of Their responses were as follows: Table 1 Star Wars Battlefront Fallout 4 Star Wars Battlefront Star Wars Battlefront Fallout 4 Fallout 4 From the data in Table 1 above, construct a Frequency Table. (10 marks) Based on your Table in Part, graphically present the information using a pie chart. (12 marks) Explain the difference between a qualitative variable and a quantitative variable and provide an example of each. (8 marks) Describe 3 ways in which understanding statistics helps us make informed decisions. (9 marks) Explain the difference between descriptive and inferential statistics. (11 marks) Question 2 (50 marks) The following are the number of minutes late that the commuter train from Kildare to Heuston station has been in the last two weeks. Assume this data is population data. Table Calculate the mean, mode and median of the dataset in Table 2. (9 marks) List three properties of the arithmetic mean. (6 marks) Construct a frequency table and a cumulative frequency table based on the data provided in table 2. (8 marks) Construct an Ogive based on your cumulative frequency table in part (11 marks) Calculate the standard deviation based on your frequency table in Part and interpret your answer. (16 marks) Page 2 of 5

3 Question 3 (50 marks) Table 3 below shows the number of hours spent exercising per week by a sample of individuals. Class Table 3 * Up to but not including 2 (f) Frequency 0 to 2* 6 2 to to to to to 12 2 What type of table is Table 3? (2 marks) Construct a line graph based on the data provided in Table 3. (12 marks) Comment on your graph from part. (2 marks) Calculate the mean for grouped data from Table 3. (12 marks) Explain the difference between the mean and the median as measures of central tendency. (6 marks) Calculate the standard deviation based on the data in Table 3 and interpret your answer (16 marks). Question 4 (50 marks) Consider students arriving at the NCI on a given day. 10% of the group decide to leave within the first hour and do not attend class. 45% go to class. The remaining students go to the library. Of those who attend class, 50% are business students, the remainder are education students. Of those who go to the library, 80% are business students and the remainder are education students. Of the business students who go to class, 60% are female and of the education students who go to class, 55% are female. Of the education students who go to the library, 40% are male. Of the business students who go to the library, 25% are male. (i) Illustrate this information on a probability tree. (12 marks) (ii) What is the probability that a student arriving into the NCI will be an education student and attend the library? (1 mark) (iii) What is the probability that a student arriving into the NCI will be female and attend class? (3 marks) Page 3 of 5

4 Work out the probability for each of the following scenarios: (i) A furniture manufacturer designed six lamp bases and five lampshades that could be used together. How many different arrangements of base and shade can be offered? (4 marks) (ii) Airlines monitor the causes of flights arriving late. A total of 75% of flights are late because of weather, while 35% of flights are late because of ground operations. A full 15% of flights are late because of weather and ground operations. What is the probability that a flight arrives late because of weather or ground operations? (6 marks) (iii) A supplier delivers an order for 30 desks to a store. By accident, three of the desks are damaged. What is the probability that the first two desks sold will be returned because they are damaged? (6 marks) (i) Explain two reasons why you would use a sample rather than the entire population in a survey. (6 marks). (ii) Briefly explain cluster sampling and systematic random sampling (12 marks) Page 4 of 5

5 Formulae Page 5 of 5