The Association of Business Executives Certificate



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questions

(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)



  1. (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)



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




    1. 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)



  1. 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)



  1. 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)



  1. 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.




  1. 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)



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




    1. Mutually exclusive events




    1. Non-mutually exclusive events




    1. Independent events




    1. Dependent or non-independent events

(v) Complementary events (20 marks)





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