Data Science Report: Comprehensive Dataset Summary and Analysis

This report presents a comprehensive analysis of a dataset, encompassing various statistical measures and their interpretations. It begins with a summary table, providing key descriptive statistics such as mean, standard error, median, mode, and standard deviation for different variables. The analysis explores relationships between variables, including the examination of p-values to assess the significance of relationships and correlation coefficients to quantify the strength and direction of linear associations. The report includes the application of ANOVA and t-tests to compare means and determine the impact of different factors. Furthermore, the report delves into the application of statistics in business and economics, explaining the role of statistics in economic problem-solving, operations, HRM, information systems, and finance. It also explains the meaning of p-values and how to interpret them, offering a valuable resource for students studying data science and related fields.

Dataset summary
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Table of contents
INTRODUCTION...........................................................................................................................3
REFERENCES..............................................................................................................................10
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INTRODUCTION
Question 1
1 1
Mean
1.46464
6 Mean
1.46464
6
Standard Error
0.05038
1 Standard Error
0.05038
1
Median 1 Median 1
Mode 1 Mode 1
Standard Deviation
0.50128
7 Standard Deviation
0.50128
7
Sample Variance
0.25128
8 Sample Variance
0.25128
8
Kurtosis -2.02051 Kurtosis -2.02051
Skewness
0.14395
9 Skewness
0.14395
9
Range 1 Range 1
Minimum 1 Minimum 1
Maximum 2 Maximum 2
Sum 145 Sum 145
Count 99 Count 99
Confidence
Level(95.0%) 0.09998
Confidence
Level(95.0%) 0.09998
b) it can be identified from p value that the there is no relationship between variables. This is
because it can be clearly seen that there is no relation between version and buy by students.
c) the correlation coefficient r is 0.0010 that shows there is no relation between mean of both X1
and X2.
Question 2
1 1035
3

Mean
1.44444
4 Mean
943.313
1
Standard Error
0.05019
5 Standard Error
10.6515
5
Median 1 Median 947
Mode 1 Mode 937
Standard Deviation
0.49943
3 Standard Deviation
105.981
6
Sample Variance
0.24943
3 Sample Variance
11232.0
9
Kurtosis -1.98905 Kurtosis
0.20936
2
Skewness
0.22706
2 Skewness -0.31992
Range 1 Range 512
Minimum 1 Minimum 665
Maximum 2 Maximum 1177
Sum 143 Sum 93388
Count 99 Count 99
Confidence
Level(95.0%) 0.09961
Confidence
Level(95.0%)
21.1376
5
b) it can be identified from p value that the there is no relationship between variables. This is
because it can be clearly seen that there is no relation between version and how much is spend by
students.
c) the correlation coefficient r is 6.275 that shows there is no relation between mean of both X1
and X2.
Question 3
a)
2 1096
Mean -69.7879 Mean
1072.18
2
Standard Error
16.6535
2 Standard Error
13.6233
1
4

Median -41 Median 1099
Mode -35 Mode 1074
Standard Deviation
165.700
4 Standard Deviation
135.550
2
Sample Variance
27456.6
4 Sample Variance
18373.8
6
Kurtosis -0.97175 Kurtosis -0.38552
Skewness -0.24178 Skewness -0.27903
Range 590 Range 602
Minimum -393 Minimum 731
Maximum 197 Maximum 1333
Sum -6909 Sum 106146
Count 99 Count 99
Confidence
Level(95.0%)
33.0483
7
Confidence
Level(95.0%)
27.0350
2
b) it can be identified from p value that the there is no relationship between variables. This is
because it can be clearly seen that there is no relation between change in income and how much
is spend by students.
c) the correlation coefficient r is 4.44 that shows there is no relation between mean of both X1
and X2.
d) Y= mx +c
e)
question 4
a) new version
1) 945. 4
2) 10.83
b) old version
1) 943.5
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2) 10.67
question 5
a) 0.98
b) 0.97
question 6
a)
ANOVA
df SS MS F
Significan
ce F
Regressio
n 1
2.84734
5
2.84734
5
12.6816
5 0.000574
Residual 97
21.7789
2
0.22452
5
Total 98
24.6262
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b) It can be interpreted from above table that the significance value obtained from P= 0.00 that is
less than P= 0.05. it clearly shows that there is no relation between version and would you buy.
c) In this the two cases are new and old version which help in finding out relation between
variable version and would you buy.
d) Here, it can be found that the case of new version had been resulted in lower P value. This is
because in this it is found that there is no relationship between them. Along with it, student
having old version said no to buy new version. So, reason is that people does not prefer to buy
new version.
question 7
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a)
ANOVA
df SS MS F
Significan
ce F
Regressio
n 1
4.56415
8
4.56415
8
22.2798
9 7.85E-06
Residual 98
20.0758
4
0.20485
6
Total 99 24.64
b) It can be interpreted from above table that the significance value obtained from P= 7.85 that is
more than P= 0.05. it clearly shows that there is relation between version and how much would
you pay to buy. Thus, high amount is paid to buy a new version.
c) In this the two cases are new and old version which help in finding out relation between
variable version and would you buy.
d) Here, it can be found that the case of old version had been resulted in lower P value. This is
because in this it is found that there is relationship between new version and how much is paid
for buying it. Along with it, student having old version said yes to buy new version. So, reason is
that they prefer to buy new version and ready to pay huge amount as well.
question 8
a)
t-Test: Paired Two Sample for Means
2 1096
Mean
-
69.7879
1072.18
2
Variance
27456.6
4
18373.8
6
Observations 99 99
7

Pearson Correlation
0.68385
4
Hypothesized Mean
Difference 0
df 98
t Stat
-
92.4334
P(T<=t) one-tail
1.92E-
97
t Critical one-tail
1.66055
1
P(T<=t) two-tail
3.84E-
97
t Critical two-tail
1.98446
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b) from table it can be found that pearson correlation is 0.68 that means there is relation between
change in income and how much is paid to buy. It means that if there is change in income than
there is also change in pay amount. Apart from it, t stat value is -92.4 and one tail t test value is
1.66.
c) In this the two cases are new and old version which help in finding out relation between
variable version and would you buy.
d) Here, it can be found that the case of old version had been resulted in lower P value. This is
because in this it is found that there is relationship between new version and how much is paid
for buying it. Along with it, student having old version said yes to buy new version. So, reason is
that they prefer to buy new version and ready to pay huge amount as well.
Question 9
What is statistics
It is science with developing and studying method for collection of data in large quantity
and analyzing, interpreting and presenting empirical data (Aslam, 2020). Statistics is a highly
interdisciplinary field; research in statistics finds applicability in virtually all scientific fields and
research questions in the various scientific fields motivate the development of new statistical
methods and theory. In developing methods and studying the theory that underlies the methods
statisticians draw on a variety of mathematical and computational tools.
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What is business statistics
It refers to process of analysing, categorising and interpreting data in order to obtain
useful info. With help of that business administrative are able to take effective decisions. There
are different statistical models which is used in interpreting data and info. By interpreting the
results of statistical modeling, business administrative professionals provide their organization
with critical insights into the current health of the company. Moreover, they can use statistics to
anticipate the future growth of the business, a concept known as inferential statistics (Cervino,
and Cicciù, 2020).
Statistics and application of it in business and economics
There are many applications of statistics is business and economics. They are defined as
below :
Economics- the statistical data is used to find out what is economic problem and also to develop
and form economic policies. Besides, integration of stats with economics is called as
econometrics that is used to solve various issues related to economy.
Operations- In this statistics plays a very useful role at the input stage
through sampling inspection and inventory management, in the process
stage through statistical quality control and six sigma method.
HRM- Statistics helps in collecting, storing, retrieval and analysis of a
mass of data. All these functions can be performed efficiently and
effectively with the help of statistics (Roy, 2017).
Information system – IT and statistics are related to each other. In that statistics is used to
improve various areas such as server time, assessing performance of program, etc.
Finance- There are many ways in which statistics is used in finance. Here, forecasting is done by
analysing data, risks are identified through it, etc.
P value and how to interpret them
Basically, P value is statistics means that how likely if null or alternate hypothesis is true
or false. The standards P value is P= 0.05 (Spiegelhalter, 2019). The value is interpreted by
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doing various types of test such as T test, regression, correlation, etc. Thus, if P value comes less
than 0.05 it means null hypothesis is rejected and if more than hypothesis is accepted.
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REFERENCES
Books and journals
Aslam, M., 2020. On detecting outliers in complex data using Dixon’s test under neutrosophic
statistics. Journal of King Saud University-Science, 32(3), pp.2005-2008.
Cervino, G. and Cicciù, M., 2020. SARS-CoV-2 persistence: Data summary up to Q2
2020. Data, 5(3), p.81.
Roy, C.J., 2017. Summary of data from the sixth AIAA CFD drag prediction workshop: case 1
code verification. In 55th AIAA Aerospace Sciences Meeting (p. 1206).
Spiegelhalter, D., 2019. The art of statistics: learning from data. Penguin UK.
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