Statistics Report: Statistical Analysis of Domestic Beer Data

This report presents a statistical analysis of a domestic beer dataset, employing various statistical tools to understand the data's characteristics and distribution. The analysis begins with constructing and interpreting box plots to visualize data distribution based on key numerical values like minimum, maximum, quartiles, and median, revealing insights into the alcohol percentage, calorie content, and carbohydrate levels of different beer brands. The report then proceeds to construct and interpret histograms for the same variables, providing a visual representation of the frequency distribution and identifying whether the data follows a symmetric or skewed distribution. Finally, the report compares data characteristics to theoretical properties using rank, percentile, and Z-scores, constructing a normal probability plot (quantile-quantile plot) to assess the data's adherence to a normal distribution. The analysis aims to provide a comprehensive understanding of the dataset, highlighting the utility of these statistical tools in data interpretation and decision-making within the context of business statistics.

Statistics

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
(a) Constructing a box plot..........................................................................................................1
(b) Constructing a histogram.......................................................................................................3
(c) Comparing data characteristics to theoretical properties.......................................................7
(b) Constructing a normal probability plot (quantile - quantile plot)........................................15
CONCLUSION..............................................................................................................................17
REFERENCES..............................................................................................................................18

INTRODUCTION
Business statistics may be swerved as a science that facilitates good decision making at
the time of uncertainty. By employing the tool of business statistics analyst can perform financial
analysis and solve issues related to econometrics, auditing, production as well as operations.
Further, normal distribution is the main parts of probability which in turn clearly reflects the
extent to which values are above or below the average level. Mean and standard deviation is the
main elements of such bell curve graph. The present report is based on the data set of domestic
beer which will provide deeper insight about several statistical tools such as box plot, histogram
and quantile-quantile (QQ plot).
(a) Constructing a box plot
Box plot is the standard way of presenting data set on the basis of five key numbers such
as minimum, maximum, Q1, Q3 and median. Hence, box plot method helps in depicting group of
data graphically through the means of quartiles. Such plots also provide high level of assistance
in indicating or showing variability that is outside the upper or lower quartiles (Box or Whisker
Plot, 2017). Further, by using or creating box plots one can present the variations which take
place in a sample of statistical population without making any assumption of statistical
distribution. In this, difference which takes place dispersion of
Particulars Alcohol % Calories Carbohydrates
Median 4.9 151.0 12.1
Quartile 1 4.4 129.0 8.6
min 0.4 55.0 1.9
max 11.5 330.0 32.1
quartile 3 5.6 166.0 14.6
mean 5.2 154.7 12.1
Alcohol %

0
1
2
3
4
5
6
Alchol%
n= 145
Bin range
Calories
0
1
2
3
4
5
6
7
8
9
10
Calories
n= 145
Bin range
Carbohydrates

0
20
40
60
80
100
120
140
160
180
200
Carbohydrates
n= 145
Bin range
Interpretation: The above depicted box plot clearly shows that in the case of alcohol%
mean and median accounts for 5.2 & 4.9%. Besides this, quartile 1 and 2 of data set implies for
4.4% & 5.6%. Range of alcohol % is g 11.1% significant which is the difference of higher and
lower value. Referring such box plot, it can be stated that data set does not fall into the category
of normal standard distribution. Moreover, in the case of normal standard both lower and upper
whisker is equal. Hence, it can be seen in the above box plot that lower whiskers of alcohol % is
higher as compared to upper so it is not considered as normal standard distribution.
Along with this, data of calories and carbohydrates does not consider as normally standard
distributed. Moreover, box plot of calories presents that lower whisker is longer than the upper one.
Descriptive statistics of data set pertaining to calories show that Q1, Q2 and Q3 are 129.0, 121.1 & 166
significantly. Further, minimum and maximum value of data set is 55 & 330. On the other side, data set of
carbohydrates exhibits that minimum and maximum value is 1.9 and 32.1 respectively. Further, it has
assessed from evaluation that average and median value of carbohydrates is similar such as 12.41. In
addition to this, tabular presentation shows that value of carbohydrates is increased from 1st quarter to the
3rd one. Hence, considering the situation of box plot, it can be mentioned that data of calories and
carbohydrate does not have normal standard distribution.
(b) Constructing a histogram
Histogram is the most effectual tool that presents the distribution of numerical data set
and helps in understanding the same. It presents estimated probability distribution of a
continuous variable. For constructing histogram, it is highly required for analyst to determine the

bin values that represents the division of entire range into a series of intervals. Hence, histogram
facilitates structured presentation of large data set and helps in decision making. Symmetric and
non-symmetric are the main two situations that histogram presents on the basis of data set needs
to be assessed (Histograms, 2017). Under symmetric distribution, two parts of the histogram
shows highly perfect representation in relation to each other. On the other, non-symmetric
distribution is also known as skewed one that does not present mirror imaging. Under skewed
distribution, there is one tail that attracted our in relation the next tail.
Alcohol % Frequency
0.4 1
1.3 0
2.3 0
3.2 2
4.1 10
5.0 78
6.0 30
6.9 7
7.8 8
8.7 4
9.7 2
10.6 2
More 1

0.4 1.3 2.3 3.2 4.1 5.0 6.0 6.9 7.8 8.7 9.7 10.6 More
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
Histogram
Frequency
Bin
Frequency
Calories Frequency
55 1
78 2
101 8
124 23
147 27
170 49
193 12
215 10
238 8
261 0
284 1
307 1
More 3

55 78 101 124 147 170 193 215 238 261 284 307 More
0
5
10
15
20
25
30
35
40
45
50
55
Histogram
Frequency
Bin
Frequency
Carbohydrates Frequency
2 1
4 8
7 15
9 17
12 23
14 43
17 19
20 9
22 6
25 2
27 1
30 0
More 1

2 4 7 9 12 14 17 20 22 25 27 30 More
0
5
10
15
20
25
30
35
40
45
50
Histogram
Frequency
Bin
Frequency
Interpretation: By preparing histograms, it has assessed carbohydrate element of most of
the brands be fall on the right side of mean such as 12.1 significantly. By considering this, it can
be presented that data set is positively skewed. Along with this, histogram of alcohol % and
calories also clearly shows that large number of brands fall into the right side which in turn
clearly presents that data set comes under the category non-symmetric distribution.
(c) Comparing data characteristics to theoretical properties.
Alcoho
l % Ranks
Percentil
e of
Alcohol
%
Z
score
of
Alcoho
l %
0.4 1 0.00345 -

2.7018
2.4 2 0.01034
-
2.3136
2.8 3 0.01724
-
2.1144
3.8 4 0.02414
-
1.9749
3.8 4 0.02414
-
1.9749
3.9 6 0.03793
-
1.7752
4.1 7 0.04483
-
1.6972
4.1 7 0.04483
-
1.6972
4.1 7 0.04483
-
1.6972
4.1 7 0.04483
-
1.6972
4.1 7 0.04483
-
1.6972
4.1 7 0.04483
-
1.6972
4.1 7 0.04483
-
1.6972
4.1 14 0.0931
-
1.3219
4.2 15 0.1
-
1.2816
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069 -

1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.2 16 0.1069
-
1.2432
4.3 29 0.19655 -0.854
4.3 29 0.19655 -0.854
4.3 29 0.19655 -0.854
4.3 29 0.19655 -0.854
4.4 33 0.22414
-
0.7583
4.4 33 0.22414
-
0.7583
4.4 33 0.22414
-
0.7583
4.4 33 0.22414
-
0.7583
4.4 33 0.22414
-
0.7583
4.5 38 0.25862
-
0.6476
4.5 38 0.25862
-
0.6476
4.5 38 0.25862
-
0.6476
4.5 38 0.25862
-
0.6476
4.6 42 0.28621
-
0.5645
4.6 42 0.28621
-
0.5645
4.6 42 0.28621
-
0.5645
4.6 42 0.28621
-
0.5645
4.6 46 0.31379
-
0.4851
4.7 47 0.32069
-
0.4658
4.7 48 0.32759
-
0.4466

4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.7 49 0.33448
-
0.4276
4.8 61 0.41724 -0.209
4.8 62 0.42414
-
0.1913
4.8 62 0.42414
-
0.1913
4.8 62 0.42414
-
0.1913
4.8 62 0.42414
-
0.1913
4.8 62 0.42414
-
0.1913
4.8 62 0.42414
-
0.1913
4.9 68 0.46552
-
0.0865
4.9 68 0.46552
-
0.0865
4.9 68 0.46552
-
0.0865
4.9 68 0.46552
-
0.0865