"Fair and Lovely" is a well-known health care and beauty company based in Sydney Australia. The company produces and markets three products lines
1. Toothpaste,
2. Body Lotion and
3. Face Wash.
Table 1 provides monthly data for a 2-year period for the following:
1. Monthly turnover for each product line
2. Monthly advertising costs
You are required to complete the following tasks in order to develop your understanding on measures of central tendency, measures of dispersion of the data and measures of association between different variables.
1. Identify the type of the data also identify the variables.
2. Organise the data into appropriate class intervals and present the following:
a. A histogram of the frequency distribution
b. An "Ogive" of the cumulative frequency distribution
c. Frequency Polygon
3. Estimate the Mean, Median, Range, Standard Deviation and Coefficient of Variation
4. Compare the risk (or variability of revenues) from three different products sales based on monthly revenue data.
5. Calculate the 25th, 50th, and 75th percentile of the first year data on advertising costs.
6. The marketing manager of Fair and Lovely has proposed to the CEO, that they invest more money on advertising in order to increase the return of the company. How can you as a analyst reporting to the CEO of the company use this statistical data to evaluate the marketing managers proposal? (Hint: 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.
|
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
|
30
|
32
|
12
|
|
July
|
22
|
31
|
35
|
13
|
|
August
|
25
|
38
|
38
|
14
|
|
September
|
32
|
38
|
42
|
15
|
|
October
|
37
|
40
|
44
|
17
|
|
November
|
38
|
46
|
47
|
22
|
|
December
|
38
|
47
|
50
|
23
|