The Association of Business Executives Certificate

(Total 25 marks)

IQM0608 6

Q6 The number of books sold each week from a small book shop over a period of 40 weeks is presented below:

231	235	234	232	245	212	244	238	218	251
233	243	255	249	224	228	249	231	221	225
210	217	246	221	230	235	219	212	223	254
238	226	219	241	233	224	228	232	223	253

1. 
   Arrange this sales data in a grouped frequency distribution table using class intervals
   

of 210 to 219, 220 to 229, 230 to 239, 240 to 249 and 250 to 259. (3 marks)

2. 
   (i)Using this grouped frequency distribution table, draw a fully labelled histogram of the weekly sales of books and comment on its shape.
   

(ii) Use this histogram to determine the most likely value of the mode. (9 marks)

3. 
   Again using the grouped frequency distribution data tabulated in answer to part (a), calculate the:
   

9. 
   mean
   

(ii) standard deviation (7 marks)

(d) Define the following terms: “mean”, “median” and “mode” . (6 marks)


(Total 25 marks)

[Turn over

7 IQM0608

(10 marks) (Total 25 marks)
Q7 The revenue R (£’000) of a manufacturing firm producing paint can be calculated using the following equation:
R = 200x – 2.5x ²

where x is the quantity of paint sold in 1000 litres.

The production costs C (£’000) of the same manufacturing firm can be calculated using the following equation (where x is the quantity of paint produced in 1000 litres):

C = 2000 + 40x

1. 
   Using the cost equation, identify the value of fixed costs (i.e. those costs that remain
   

constant irrespective of the quantity of paint produced). (2 marks)

2. 
   Using values of x from 0 to 35 in intervals of 5 units, construct a table to calculate the values of C and R, and use this data to plot a fully labelled graph for C and R against x.
   

(Use the graph paper at the front of your answer book.) (11 marks)

3. 
   From this graph, estimate the quantity of paint produced where the firm breaks even
   

(that is, neither makes a profit nor a loss). (2 marks)

4. 
   The same firm invests in new production processes which alter the company’s production costs C (£’000) so that there is a new cost equation:
   

C = 2500 + 30x

1. 
   Comment on how this investment has altered the firm’s cost structure.
   

2. 
   Assuming that the revenue equation remains the same, that is,
   

R = 200x – 2.5x ², use this new cost equation to calculate the level of paint
production that is now required for the firm to break even.

IQM0608 8

Q8 (a) Distinguish between the following terms:

1. 
   Continuous and discrete variables (Give examples.)
   

(ii) Primary and secondary data (5 marks)

2. 
   Explain, using examples, what is meant by each of the following types of events in probability:
   

1. 
   Mutually exclusive events
   

2. 
   Non-mutually exclusive events
   

3. 
   Independent events
   

4. 
   Dependent or non-independent events
   

(v) Complementary events (20 marks)