IDBQM001 Quantitative Methods for Business Exemplar Examination
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THE NCUK INTERNATIONAL DIPLOMA IN BUSINESS
Exemplar Examination
Quantitative Methods for Business
Section A
Answer ALL Questions
Question A1
The table below shows the hourly fees of 80 consultants:
|
Fee (£/hour) |
Number of consultants |
|
< 40 |
20 |
|
40 < 50 |
10 |
|
50 < 60 |
25 |
|
60 < 70 |
10 |
|
70 < 80 |
5 |
|
80 < 90 |
5 |
|
90 < 100 |
5 |
|
a) What percentage of consultants charge at least £70/hour? b) Which of the class intervals contains the median fee? c) Estimate the lower quartile fee d) Which average (mean, median or mode) might be estimated using the midpoints of the frequency distribution? |
[ 2 ] [ 2 ] [ 1 ] [ 1 ] |
Question A2
A survey of staff wages gave the following frequency distribution and histogram:
|
100
80
60
40
20
0 |
Wages of staff
|
a) How many staff had wages between £24 and £30? [ 2 ]
b) Approximately how many staff have a wage between £18.50 and £23? [ 2 ]
c) The number of staff earning between £22 and £24 had increased by 25% from [ 1 ] the previous year. How many staff were in this wage band in the previous year?
Question A3
a) A student has marks of 48%, 63%, 68%, 71% and 72% in five of her six [ 2 ]
subjects . What does she need to score in the 6th subject to obtain an overall average (mean) of 70%?
b) The lower quartile of a distribution (Q1) = 50 and the upper quartile (Q3) = [ 4 ]
100. For each of the following statements, write down whether it must be true or not.
i. The median is 75.
ii. The mean is between 50 and 100.
iii. The median is between 50 and 100.
iv. The standard deviation cannot be more than 50.
Question A4
The demand function for a product is given by P = 50 – 2Q. The total cost TC = 160 + 2Q.
a) Write down expressions for TR and Profit [ 2 ]
b) Find the maximum profit and the output that maximises the profit. Confirm that [ 3 ] it is a maximum.
c) Find the maximum revenue and the output that maximises revenue. [ 2 ]
Question A5
The marginal cost for a product is given by MC = 10/Q
b) If total costs are 500 when Q = 10, find the equation of the total cost function. [ 4 ]
Question A6
Two travel websites ranked eight different airlines as follows: [ 6 ]
|
Airline |
Rank in website 1 |
Rank in website 2 |
|
|
Singapore Airlines Emirates Cathay Pacific Air France KLM Lufthansa British Airways American Airlines |
1 2 3 4 5 6 7 8 |
3 2 1 7 8 5 4 6 |
|
Use Spearman’s rank correlation to investigate the data and comment on your results.
Note:
rs = 1 - 
where, for each observation, d is the difference between the X and Y ranks.
Section B
Answer TWO Questions ONLY.
Question B1
The frequency distribution and Excel output below represents the results of a survey in wages in the North and South regions of a country.
|
Wage (£) |
North |
South |
|
160 < 200 200 < 220 220 < 240 240 < 260 260 < 300 300 < 400 |
28 58 69 44 26 15 |
10 21 35 75 64 35 |
|
Total |
240 |
240 |
|
120 100 80 |
C.F. Curves |
|
|
|
|
40 20 0 |
|
|
160 200 240 280 320 360 400 Wage (£) |
|
North |
South |
||
|
Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness |
??? 4.17 ??? 230 45.68 2086.39 0.87 1.11 |
Mean |
263 42 |
|
Standard Error Median |
4.06 250 |
||
|
Mode |
250 |
||
|
Standard Deviation Sample Variance Kurtosis |
44.50 1980.67 ‐0.01 |
||
|
Skewness |
0.64 |
||
a) Use the table above and any information from the Excel output to answer the following:
i. Calculate an estimate of the mean wage in the North. [ 5 ]
ii. Estimate the median wage in the North to the nearest £10 [ 1 ]
iii. Use the descriptive statistics, charts and graphs to make relevant [ 3 ] comparisons between wages in the North and the South regions.
Question B1 continued
b) The population of eight cities and the amount of open space (parks, etc) in each are shown in the table and spreadsheet regression output below:
|
City |
A |
B |
C |
D |
E |
F |
G |
H |
|
Population (millions) |
2 |
6 |
8 |
8 |
12 |
16 |
20 |
20 |
|
Open space (hectares) |
58 |
105 |
88 |
2023-06-05