BDM 2 - 15 Dec 2009
Transcript of BDM 2 - 15 Dec 2009
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Task 1
A brewing company wishes to launch a new canned lager to the market. It has close links
with a major supermaket chain which will only permit a promotion of the lager in two of
its store. The two selected stores, Store A and Store B, monitor their sales of all brands of
canned lager over a weekend period with the following results:
Sales value of
lager (USD)
Frequency
Store A Store B
0-2.5 27 1
2.5-5 114 3
5-7.5 333 31
7.5-10 530 142
10-12.5 504 328
12.5-15 334 498
15-17.5 121 504
17.5-20 29 351
20-22.5 5 110
22.5-25 2 29
25-27.5 1 3
Total 2,000 2,000
Based on the frequency distribution above, we can see that most of times the
frequency in store A has lower sales value than in store B. More than half of times the
frequency in store A have the sales values are less than $10 while in store B there is
50% of times in which the sales value is higher than $15. However, we should
canculate the mean customer expenditure to get the whole set of data because the
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value of every items is included in the computation of the mean. The mean consumer
expenditure in each store is calculated from the sum of values of items divided by the
number of items. After caculating, weve got that the mean consumer expenditure for
store A is 10.07 and for store B is 14.93. The mean in store B is more reliable than in
store A in conclusion.
In order to know more about the variability of customer, we have to compute the
quartile range, variance, standard deviation and the coefficient of varation.
Quartiles are one mean of indentifying the range within which most of the values in
the population occur. To get the quartile range we can canculate the two quartiles: Q1
(the 25th percentile), Q3 (the 75th percentile) and then take Q3 minus Q1. After
canculating, for store A, we have the quartile range is 4.84 while in store B is 5. That
means the range of values of the middle half of the population for store A is 4.84 and
for store B is 5.01.
Variance is a statistical parameter shows the extent to which a set of values depart
from uniformity. In other words, the variance is the average of the squared mean
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deviation for each value in a distribution. For store A, we canculated the variance is
12.86 and for store B is 13.25. This means that the sales value of lager are nearly
gathered around 12.86 in store A and 13.25 in store B.
Standard deviation is the square root of the variance. Instead of taking the absolute
value of the difference between the value and the mean to avoid the total of the
differences summing to zero, we can square the differences. Then, we get the vairance
and from that we get the most important measure of dispersion in statistics, the
standard deviation.
After that, we use the coefficient of variation to compare the dispersion of two
distributions. The coefficient of variation indicates how large the standard deviation is
in relation to the mean. After calculating, we get the coefficient of variation is 0.36
for store A and 0.24 for store B. The bigger the coefficient of variation, the wider the
dispersion. As the result above, we can conclude that store B has a wider dispersion
than store A.
In conclusion, store B seems to have a better opportunity for becoming a successful
promotion of the new larger. Compare the skewness between the two store, we can
see that in store B, the skewness shows a symmetrical frequency distribution with the
well-proportioned shape; while in store A, the graph leans towards the left hand side,
with the tail stretching out to the right.
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Besides that, the mean of store B is higher than store A (store B: 14.93; store A:
10.07). That means the avarage values of store B is higher than store A. Because of
those reasons, if we have to choose one store to be enlarged, we should choose store
B.
Task 2
To help determine how many beers to stock, the manager of a club wanted to know
how the temperature affected beer sales. Accordingly, she took ten records of beer
sales at different temperature and listed below:
Temperature
(
0
C)
Sale volume of beer
(litres)
27 20,533
20 1,439
26 13,829
26 21,286
31 30,985
23 17,187
30 30,240
33 37,596
25 9,610
29 28,742
From these data above, wa can draw a scattergraph as follow:
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It is easy to realize the trend is that the higher temperature is, the more sale volumes
are sold. Then, to predict values for one variable (y) given values for the other
variable (x), we need to find a line which is best fits for all the points on scattergraph
above. After calculating, the linear regression that best fits upper data is :
Y= -51.23 + 2.68 * X
1 = 2.68means that when the temperature increase 10C, the sale volume of beer willrises correlatively an average of 2.68 litters. Besides that,1is a positive number
means that the relation between sale volume and temperature is positively
corresponsive.
o=-51.23 means that except the temperature, there is no reasons to make the sale
volume change into -51.23. o is a negative number, in order to have a positive
volume of sales, 1 * X should be a positive number. Therefore, in case the
temperature is less than 200C, no one will drink beer, based on the linear regression.
Use the regression equation to estimate sale volumes of beer when the temperature
changes, we have a table below:
Temperature Sale volume
28 23.83
32 34.55
35 42.5939 53.31
These forecast is very reliable because that the relationship between temperature and
beer sales has strong linear relationship. The correlation coefficient (R) between
temperature and sales is 0.94. The correlation coefficient measures the degree of
correlation between two variables. The more R is closer to 1, the stronger linear
relationship between X and Y. Therefore, the variables are closed to perfectly
positively correlation. It means that this relationship doesnt have function between Xand Y but the trend is nearly the same.
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Task 3
The area sales manager of a company is responsible for providing a forecast for the
value of sales. However, she is ill and asks you to help her. To assit your task, she
gives you the quarterly figures on unit sales for the last four years as follows:
Unit sales 2004-07
(million VND)
Year Q1 Q2 Q3 Q4
2004
2005
2006
2007
441.1
476.4
580.7
692.0
397.7
454.4
573.2
676.5
396.1
450.8
571.6
659.9
472.8
553.5
703.6
752.8