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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