Assume that XYZ is a renowned chemical company in a particular country. The company is currently producing and marketing three products including Toothpaste, Body lotion and Face wash. The monthly data for two years on total revenue of each product are shown in Table 1. Monthly advertisement costs of all three products are also given in the same Table.
Students are required to complete the following tasks and practice by themselves (individually) in order to develop their understanding on measure of central tendency, measure of dispersion of the data and measure of association of different variables.
i. Identify the type of the data also identify the variables.
ii. Organise the data into appropriate class intervals and present the following:
• A histogram of the frequency distribution
• An “Ogive” of the cumulative frequency distribution
• Frequency polygon
iii. Estimate the Mean, Median, Range, Standard Deviation and Coefficient of Variation
iv. Compare the risk from three different products sales based on monthly revenue data.
v. Calculate the 25th, 50th, and 75th percentile of the first year data on advertisement.
vi. The marketing manager of XYZ Company proposed the CEO to invest more money on advertisement in order to increase the return of the company. Do you think the marketing manager of the company can prove that his proposed plan for new investment is justified?
(Hints: Calculate correlation coefficient between revenue data of each product and advertisement costs)
Table 1. Monthly returns and costs on advertisement (in thousand dollars) of XYZ Company for two years
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|
|||||
|
Year |
Months |
Toothpaste (AU$) |
Body Lotion (AU$) |
Face wash (AU$) |
Advertisement Costs (AU$) |
|
Year 1 |
January |
45 |
51 |
57 |
28 |
|
February |
48 |
57 |
61 |
28 |
|
|
March |
50 |
61 |
61 |
29 |
|
|
April |
52 |
62 |
67 |
30 |
|
|
May |
54 |
67 |
68 |
34 |
|
|
June |
41 |
49 |
51 |
24 |
|
|
July |
71 |
98 |
132 |
44 |
|
|
August |
76 |
104 |
132 |
50 |
|
|
September |
81 |
132 |
137 |
57 |
|
|
October |
82 |
156 |
140 |
58 |
|
|
November |
84 |
146 |
147 |
62 |
|
|
December |
85 |
152 |
148 |
63 |
|
|
Year 2 |
January |
85 |
156 |
158 |
70 |
|
February |
55 |
72 |
70 |
36 |
|
|
March |
61 |
73 |
112 |
37 |
|
|
April |
66 |
84 |
121 |
40 |
|
|
May |
70 |
95 |
123 |
43 |
|
|
June |
21 |
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