This document provides information on data analysis and report writing. It discusses topics such as data collection, processing, analysis, univariate analysis including measures of central tendency, bivariate analysis including correlation and regression, and hypothesis testing. It also outlines the structure of a research report including sections like the executive summary, introduction, methodology, findings, and provides examples of tables, charts, and data interpretation.

1. DATA ANALYSIS & REPORT
WRITING
In a class of 25 strength students have achieved following marks-
Can you answer:
a) How many students passed if passing is for 40?
b) What is the failure percentage?
c) How is the class quality?
89 33 57 78 58
45 75 25 72 68
32 82 17 60 94
17 21 69 72 64
91 67 87 68 59

2. DATA ANALYSIS
DATA ANALYSIS refers to the computation of certain measures along with
searching for patterns of relationship that exist among data groups.
• The general flow in the research process is –
a) Data Collection
b) Data Processing &
c) Data Analysis
• However Data Collection is already covered in the last chapter.

3. DATA PROCESSING
DATA PROCESSING includes-
• Editing: (Field & Office) (Completeness, Accuracy, Uniformity etc.)
• Coding: (Specify various Categories & Allocate Responses)
(Appropriate, Exhaustive, Mutually Exclusive, Single Dimension, Code
Sheet etc.)
• Classification: (According to Attributes, According to Intervals)
• Tabulation: (The logical listing of related quantitative data in vertical
columns and horizontal rows with details)

4. RULES OF DATA TABULATION
A) Rules regarding table structure-
• Table Number
• Table Title
• No of Rows & Columns
• Captions & Stubs
• Ruling & Spacing
• Column Size
• Arrangement of Items
• Table Units
• Explanatory Notes
• Source
• Totals

5. RULES OF DATA TABULATION
B) General Rules-
• Attractive Shape
• Simplicity
• Place of Approximation
• Free from Irrelevant Data
• Use of Circle or Box
• Miscellaneous Columns
• Non availability of the data

6. FREQUENCY
• Frequency:
It is the number of times a given quantity (or a group of quantities) occurs
in a set of data.
• Types of Frequency:
a) Relative Frequency
b) Cumulative Frequency &
c) Percentage Frequency
• Frequency Distribution:
a) Discrete or Ungrouped Frequency Distribution
b) Continuous or Grouped Frequency Distribution
c) Cumulative Frequency Distribution

7. DISCRETE OR UNGROUPED
FREQUENCY DISTRIBUTION
• Income of 10 peoples in the Colony-
Person Profession Income
Nasir Pvt.Employee Rs.3.5 Lac
Anand Govt.Employee Rs.2.8Lac
Sachin Business Rs.7.0Lac
Shivam Pvt.Employee Rs.4.3Lac
Tanvi Govt.Employee Rs.11.4Lac
Shravya Pvt.Employee Rs.1.8Lac
Rajiv Farmer Rs.75,000
Tina Farmer Rs.97,000
Jyoti Farmer Rs.13.6Lac
Manoj Govt.Employee Rs.8.6Lac

8. CONTINUOUS OR GROUPED
FREQUENCY DISTRIBUTION
• Income of 10 peoples in the Colony-
IncomeSlab Frequency
GE PE F B Total
Upto01Lac - - 2 - 2
01to05Lac 1 3 4
05to10Lac 1 - - 1 2
Above10Lac 1 - 1 - 2
Total 3 3 3 1 10

9. BASIC COMPONENTS OF CONTINUOUS OR
GROUPED FREQUENCY DISTRIBUTION
• Class Limits:
• Class Intervals: [C.I. =
(𝐿−𝑆)
𝐾
] [Exclusive/Continuous Class,
Inclusive/Discontinuous Class, Open Ended Class]
• Range
• Mid Value or Mid Point
• Frequency
• Number of Class Intervals: [K=1 + 3.322log10 𝑁]
• Size of Class Interval: [C=
𝑅𝑎𝑛𝑔𝑒
1+3.322log10 𝑁
] i.e.
𝑅𝑎𝑛𝑔𝑒
𝐾

10. GRAPHICAL REPRESENTATION OF
DATA
• Bar Chart
• Pie Chart
• Histogram
• Leaf & Stem
• Candle Stick
• Box Plot (Smallest Value, Lower Quartile, Median, Upper Quartile, Largest
Value)

11. TYPES OF DATA ANALYSIS
UNIVARIATE
ANALYSIS:
(Measures of Central
Tendency i.e.
a) Mean,
b) Median,
c) Mode etc. )
BIVARIATE
ANALYSIS:
a) Correlation Analysis
b) Linear Regression
c) Association of
Attributes
d) Two Way ANOVA
Multivariate
Analysis:
DESCRIPTIVE
ANALYSIS
Statistical
Estimation:
Hypothesis
Testing:
INFERENTIAL
ANALYSIS

12. UNIVARIATE ANALYSIS
MEAN:
x=
∑𝑋
𝑁
------for Individual Series
x=
∑𝑓𝑋
𝑁
------for Discrete/Ungrouped Frequency
distribution
x=
∑𝑓𝑋
𝑁
------for Continuous/Grouped Frequency
distribution

13. UNIVARIATE ANALYSIS
MEDIAN:
Md= Value of [
𝑁+1
2
]th Observation in ascending order
------for Individual
Series
Md= Value of [
𝑁+1
2
]th Observation in ascending order
------for Discrete/Ungrouped Frequency distribution
i) Find Less Than c.f.
ii) Then find median class= class to which [
𝑁
2
]th observation
belongs
iii) Md= l+
ℎ
𝑓
[
𝑁
2
− 𝑐]
(where, l-Lower Limit of Median Class, h- Size of Median Class, f-
Frequency of Median Class, C- Cumulative Frequency of Class
immediately preceding the Median Class)
------for Continuous/Grouped Frequency distribution

14. UNIVARIATE ANALYSIS
MODE:
M0= Value with maximum frequency
------for Individual
Series
M0= Value having maximum frequency
------for Discrete/Ungrouped Frequency
distribution
i) Find Modal Class i.e. class with highest frequency
then
ii) M0= l+h [ 𝑓1
−𝑓0
2𝑓1
−𝑓0
−𝑓2
−
]
------for Continuous/Grouped Frequency
distribution
Mode = [3Median -
2Mean]

15. UNIVARIATE ANALYSIS
STANDARD DEVIATION (6):
6=
1
𝑁
∑(𝑥−𝑥)2
------for Individual
Series 6=
1
𝑁
∑𝑓(𝑥−𝑥)2
------for Discrete/Ungrouped Frequency
distribution
6=
1
𝑁
∑𝑓(𝑥−𝑥)2
------for Continuous/Grouped Frequency
distribution

16. UNIVARIATE ANALYSIS
VARIANCE = (62)
COEFFICIENT OF VARIATION = 𝟔
𝑿
× 100
RANGE = L - S
QUARTILE DEVIATION =
𝟐
𝟑
𝟔
MEAN DEVIATION =
𝟒
𝟓
𝟔

17. BIVARIATE ANALYSIS
A) CORRELATION ANALYSIS:
a) Simple Correlation
b) Multiple Correlation
c) Partial Correlation
B) REGRESSION ANALYSIS :
a) Regression line of y on x
b) Regression line of x on y

18. CORRELATION ANALYSIS
KARL PEARSON’S COEFFIECIENT OF
CORRELATION (r):
rxy =
𝑪𝒐𝒗(𝒙,𝒚)
𝟔 𝒙
𝟔 𝒚
=
𝑵∑𝒙𝒚− ∑𝒙 −(∑𝒚)
√[𝑵∑𝒙 𝟐
− ∑𝒙 𝟐
][𝑵∑𝒚 𝟐
− ∑𝒚 𝟐
]
COEFFICIENT OF DETERMINATION = r2
SPEARMAN’S RANK CORRELATION COEFFICIENT
(þ):
Þ=1-
𝟔∑𝒅 𝟐
𝑵(𝑵 𝟐
−𝟏)
(where d is difference between ranks)

19. REGRESSION ANALYSIS
Regression Line of y on x:
(y- y ) = byx (x - x )
byx= 𝐫
𝟔 𝒚
𝟔 𝒙
=
𝑵∑𝒙𝒚−(∑𝒙)(∑𝒚)
𝑵∑𝒙 𝟐
− ∑𝒙 𝟐
Regression Line of x on y:
(x- x ) = bxy (y - y )
bxy= 𝐫
𝟔 𝒙
𝟔 𝒚
=
𝑵∑𝒙𝒚−(∑𝒙)(∑𝒚)
𝑵∑𝒚 𝟐
− ∑𝒚 𝟐

20. TESTING OF HYPOTHESIS/
TEST OF SIGNIFICANCE
Parametric
Test
t test
z test
f test
Non
Parametric
Test
Sign Test
Mann-
Whitney U
test
Wilcoxon
Signed Rank
Test
Run test for
Randomness
Kruskal-
Wallis Test

21. DIFFERENCE BETWEEN PARAMETRIC TESTS &
NON PARAMETRIC TESTS:
ParametricTests (Makesassumptions about
Parameters.e.g. DataisNormally/Intervally
Distributed)
Non-ParametricTests (Don’t Makes
assumptions aboutParameters. AlsoDatais
FreelyDistributed)
NormalDistributiondataisrequired. NormalDistributiondataisnotrequired.
UsesMetricdata OrdinalorIntervalScale dataisused.
Canbeapplied forbothsmall & large samples. Canbeapplied forsmall samples.
Onesample using zorttest. Onesample using theSign test.
Twoindependentsamples using atorztest. Twoindependentsamples using the Mann-
WhitneyUStatistics.
Twopairedsamples usingatorztest. Twopairedsamples usingtheWilcoxonsigned
ranktest.
Randomness-Notestavailable Randomness-Run testforRandomness
Several independentsamples usingF testin
ANOVA
Several independentsamples using Kruskal-
Wallistest.

22. HYPOTHESIS TESTING (PARAMETRIC TESTS)
Steps in Hypothesis Testing
• Setting up of a Hypothesis
• Setting up of a suitable level of significance (∝)
• Determination of test statistic
• Determination of critical region
• Computing the value of test statistic
• Making decisions/Hypothesis testing
Various Terminologies in Hypothesis Testing:
• Level of Significance
• Confidence Level
• Critical Region
• Acceptance Region
• Normal Distribution

23. HYPOTHESIS TESTING (PARAMETRIC TESTS)
Various Test Statistics:
a) t test; b) z test; c) p test
a) t test: (Used when sample is small i.e. <30 and S.D. is not known)
𝒕 𝒏 − 𝟏 =
𝒙 − µ 𝑯𝟎
𝟔𝒙
b) z test: (Used when sample is large/small i.e. ><30 and S.D. is known)
Z=
𝒙−µ 𝑯𝟎
𝟔/√𝒏
c) p test: (Alternate method based on probability)
In this method no need to find Critical Value (z value)
Reject Ho if p ≤ ∝
Accept Ho if p > ∝

24. HYPOTHESIS TESTING
(NON PARAMETRIC TESTS)
CHI SQUARE TEST: (Requires data in terms of frequencies)
• Chi Square test can be used when data is unsymmetrically distributed.
• A Chi Square test is used for Goodness of fit
• Chi Square test for the independence of variables
• Chi Square test for the equality of more than two population
proportions.
Chi Square= ∑𝒊=𝟏
𝑲
𝑶 𝒊 − 𝑬𝒊 𝟐/𝑬𝒊

25. RESEARCH REPORT
• A report is a statement of collected & considered facts, so drawn up as to
give clear & concise information to persons who are not in possession of the
full facts of the subject matter of the report. -
- Lancaster
• Characteristics of good research Report:
a) Accuracy; b) Clarity & Completeness; c) Appearance; d) Reliability;
e) Timeliness; f) Simplicity; g) Brevity; h) Economy and i) Logical Content
• Mechanism of Writing a Research Report/Steps in writing a Research
Report:
a. Investigating the sources of Information
b. Taking Notes
c. Analyzing the data;
d. Making an Outline

26. STRUCTURE OF A RESEARCH REPORT
1. EXECUTIVE SUMMARY:
A. BRIEF ABOUT THE PROJECT:
2. INTRODUCTION:
A. WHY TOPIC IS SO IMPORTANT?
B. BRIEF ABOUT COMPANY
C. BRIEF ABOUT YOUR PROJECT
D. WHAT YOU ARE GOING TO DO IN THE PROJECT?
3. INDUSTRY PROFILE:
A. WORLD SCENARIO
B. INDIAN SCENARIO
C. NUMBER OF COMPANIES AND THEIR PERFORMANCE

27. STRUCTURE OF A RESEARCH REPORT
4. COMPANY PROFILE:
A. HISTORY
B. VISION
C. MISSION,
D. MILESTONES
E. ORGANIZATION STRUCTURE
5. PRODUCT PROFILE:
A. BRIEF ABOUT PRODUCTS OF COMPANY IN THE AREAS
6. OBJECTIVE OF STUDY:
A. RELATED TO YOUR TITLE SET 3-5 OBJECTIVES

28. STRUCTURE OF A RESEARCH REPORT
7. RESEARCH METHODOLOGY:
A. INTRODUCTION TO RESEARCH METHODOLOGY:
B. RESEARCH TYPE:
C. PRIMARY DATA: DEFINITION OF PRIMARY DATA AND HOW YOU
COLLECTED PRIMARY DATA
D. SECONDARY DATA: DEFINITION OF SECONDARY DATA AND HOW YOU
COLLECTED SECONDARY DATA
E. SAMPLING: VARIOUS METHODS OF SAMPLING AND WHICH METHOD YOU
USED FOR SAMPLING
F. POPULATION:
G. SAMPLING AREA:
H. SAMPLING UNIT:
I. SAMPLE SIZE:
J. SCOPE OF THE STUDY: EXPLAIN FURTHER AREAS OF RESEARCH AND
IMPORTANCE OF RESEARCH
K. LIMITATIONS OF THE STUDY: EXPLAIN THE CONSTRAINTS, HURDLES
AND BOUNDARIES

29. STRUCTURE OF A RESEARCH REPORT
8. THEORETICAL BACKGROUND OF THE
STUDY:
A. MANAGEMENT THEORY RELATED TO YOUR TITLE AND REVIEW
OF LITERATURE IF ANY
9. DATA ANALYSIS AND
INTERPRETATION:
A. WRITE QUESTION
B. MAKE TABLE HAVING COLUMN OF SR. NO. , DETAILS, NO. OF
RESPONDENTS AND %
C. GIVE TABLE NUMBER AND MENTION SOURCE
D. DRAW CHARTS (IF PI- MENTION %, IF BAR MENTION FREQUENCY)
E. INTERPRETATION
10. FINDINGS:
A. INTERPRETATION AND GENERAL FINDINGS DURING RESEARCH

30. STRUCTURE OF A RESEARCH REPORT
11. CONCLUSION:
A. CONCLUDE WHOLE PROJECT IN ONE PARAGRAPH WITH MAJOR
FINDINGS & SUGGESTIONS.
12. SUGGESTIONS:
a. SUGGESTIONS AS PER THE FINDINGS
13. BIBLIOGRAPHY:
a. REFERENCES AS PER APA STYLE
14. ANNEXURE:
A. QUESTIONNAIRE
B. COMPANY REPORTS IF REFERRED
C. LIST OF RESPONDENTS
D. PHOTOGRAPHS RELATED TO VISITS IF ANY