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Business Statistics
Fixed acidity - Volatile acidity - Citric acid - Residual sugar -Chlorides
7.4 0.7 0 1.9 0.076
7.8 0.88 0 2.6 0.098
7.8 0.76 0.04 2.3 0.092
11.2 0.28 0.56 1.9 0.075
7.4 0.7 0 1.9 0.076
7.4 0.66 0 1.8 0.075
7.9 0.6 0.06 1.6 0.069
7.3 0.65 0 1.2 0.065
7.8 0.58 0.02 2 0.073
7.5 0.5 0.36 6.1 0.071
6.7 0.58 0.08 1.8 0.097
7.5 0.5 0.36 6.1 0.071
5.6 0.615 0 1.6 0.089
7.8 0.61 0.29 1.6 0.114

2. 8.9 0.62 0.18 3.8 0.176
8.9 0.62 0.19 3.9 0.17
8.5 0.28 0.56 1.8 0.092
8.1 0.56 0.28 1.7 0.368
7.4 0.59 0.08 4.4 0.086
7.9 0.32 0.51 1.8 0.341
8.9 0.22 0.48 1.8 0.077
7.6 0.39 0.31 2.3 0.082
7.9 0.43 0.21 1.6 0.106
8.5 0.49 0.11 2.3 0.084
6.9 0.4 0.14 2.4 0.085
6.3 0.39 0.16 1.4 0.08
1. For the data on 26 red wines given above, conduct the following analysis:
i. Provide five-number summary i.e. the minimum, 1st quartile, median, 3rd quartile
and maximum value for fixed acidity. Arrange them in increasing order on a straight
line, draw a box plot and interpret what it means.
ii. Calculate the correlation coefficient between fixed acidity and volatile acidity and
between residual sugar and chlorides. Comment on the strength and direction of
association for the two variable pairs.
iii. What can be stated about the cause-effect relationship between fixed acidity and
volatile acidity, based on the correlation coefficient score? (10 Marks)

3. 2. For the data in the table below:
i. What do high kurtosis and skewness figures denote?
ii. Free Sulphur dioxide and total Sulphur dioxide have mean, median and modes that
differ substantially from each other. What can you infer from this?
iii. By looking at the descriptive stats of the variables, identify two that may be closest to
being normally distributed. Why?
3. Lok Sabha in India is to discuss a key constitutional amendment, and there will be
four rounds of voting. In each round of voting, assume that the ruling party has a 60%
chance of winning, i.e. getting the resolution passed by majority vote. Further assuming
that the voting rounds are independent of each other, what is the probability that:
a. The ruling party will win 0 rounds, 1 round, 2 rounds, 3 rounds or all 4 rounds of
voting? (5 Marks)
b.The ruling party will win at least 1 round? (5 Marks)
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