Management

1. Dr. Urooj A Siddiqui

2.  Data – Raw Facts, especially numerical facts,
collected together for reference or
information.
 Data is collected on some particular
variable/s
 Data analysis is processing of data to derive
useful information
 Knowledge communicated concerning some
particular fact
 The created knowledge helps in APPLICATION /
DECISION MAKING

3.  Categorical: Qualitative
 Continuous: Quantitative
Data
Categorical
Nominal Ordinal
Continuous
Interval Ratio

4.  Any phenomenon which takes at least two
different values/ observations
 Data: Set of values/ observations
collected on variable is called data
 Nominal
 Ordinal
 Interval
 Ratio

5. 1. Data Preparation / Initial
Operations
2. Summarizing Data / Data
Analysis Operations
 Editing / Cleaning
 Coding
 Classification
 Tabulation
 Graphical
Representation
 Tables / Crosstab
 Graph / Figure
 Statistical Analysis
1. Descriptive Methods
 Frequency, %age, Ratio,
 Mean, Median, Standard
Deviation (Variance)
2. Inferential Methods
 Comparison (t/z-test/Anova)
 Association (chi square test)
 Correlation (r)
 Prediction/ Regression
(y = ax + b)

6.  Editing / Data Cleaning
 examining the collected raw data to detect any errors
and omit/correct it if possible
 Coding
 assigning numerals to answers so that responses can
be put into a limited number of categories
 Classification
 Grouping of data on some basis (large volume of raw
data is reduced into homogenous groups
I. Attribute - on the basis of demographic bases
eg. gender, rural/urban, day scholar/hosteller
II. Class Interval – on the basis on some numeric range
eg. 0-10, 10-20 etc.

7. I. Tabulation
 is the process of displaying raw data in tabular
form and summarising it for further analysis
 orderly arranging data in columns and rows
Tabulation is essential because
 It conserves space and reduces statements
 It facilitates the process of summation of
items, comparison, detection of errors and
omissions
 Basis for various statistical computations

8. Name
Gende
r
Caste Age Mob. No. Edu
Yrs in
school
IQ
Pain
level
temp of
locality
deg cel
Ram M Hindu 60 9450366367 NIL 0 16 Mild-0 -4
Akbar M Muslim 65 8004896712 HS 16 14 Mod-1 20
Sita F Hindu 305 9934876545 Int. 19 0 Mild-0 15
Shalini F Hindu 90 2542543598 HS 8 1 6 Mild-0 0
Mehnaj F Sikh 38 9458098734 UG 21 13 Severe-2 0
Ravi M Hindu 48 9412890112 PG 23 20 Mod-1 -1
Hari M Hindu 45 8796654398 Prim 12 10 Mod-1 30

9. Name Gender Caste Age Mob.No.
Edu
level
Yrs in
sch.
IQ
Pain
level
temp of
locality
deg cel
7 1 1 60 9450366367 -1 0 16 0 -4
2 1 2 65 8004896712 1 16 14 2 20
5 2 1 35 9934876545 2 19 0 0 15
4 2 1 90 2542543598 1 8 1 6 0 0
3 2 3 38 9458098734 3 21 13 3 0
6 1 1 48 9412890112 4 23 20 2 -1
1 1 1 45 8796654398 0 12 10 2 30
Nominal & Ordinal called qualitative . Interval and Ratio called quantitative

10. Single Variable Freq. Table
Age Group (years) Freq.
Below 20 2
20-22 28
22-24 16
24-26 10
Above 26 4
60
Roll.
No
Age
(yr)
1 22
2 24
3 23
4 26
5 19
6 25
. .
. .
. .
. .
. .
60 22
 Single / Multi Variable Table - one or
more variable (no interaction)
**Multiple Variable Table – as presented in above slide

11.  Crosstabs – interaction of two or more
variables
Two Variable Interaction – Crosstab
Age Group
Gender
Male Female Total
Below 20 1 1 2
20-22 18 10 28
22-24 9 7 16
24-26 7 3 10
Above 26 3 1 4
38 22 60

12. Graphical Representation of Data
 Pie Chart
 Bar Graph
 Histogram
 Line Graph
 Scatter Plot
 Scatter Plot & Correlation

13. Pie Charts
 It is used to represent %ages, distribution of 1
variable at various levels
8.2, 58%
3.2,
23%
1.4,
10%
1.2,
8%
Sales (in mn)
1st Qtr
2nd Qtr
3rd Qtr
4th Qtr

14. Bar Chart
 It is used to represent 1 variable at various levels
 Levels can be year/ groups etc.
4.3
2.5
3.5
4.5
0
0.5
1
1.5
2
2.5
3
3.5
4
2018 2019 2020 2021
Sales

15. Bar Chart
4.3
2.5
3.5
2.4
4.4
1.8
2 2
3
2.5
3
4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
2018 2019 2020
Clustered Bar
1st
2nd
3rd
4th

16. Histogram
 To show the distribution of a quantitative
variable
4
6
10
8
2 0
0
2
4
6
8
10
12
10 20 30 40 50
Frequency
Class Interval/Variable Unit

17. Line Diagram
 To show change in variable in a particular time
period / on some reference range
₹ 5.60
₹ 5.80
₹ 6.00
₹ 6.20
₹ 6.40
₹ 6.60
₹ 6.80
₹ 7.00
₹ 7.20
₹ 7.40
1 2 3 4 5 6 7 8 9 10
Stock
Price
Last 10 Days

18. Line Diagram
 May also be used to compare 2 or more variables
along the range
0
2
4
6
8
10
12
14
1 2 3 4 5 6 7 8
Adani
Tata
Reliance

19. Scatter Plot
 It is used to express relationships between two
variables
0
1
2
3
4
5
6
0 1 2 3 4
Sales in
Crore
Adv Budget in 10’Lacs
Y-Values

20. Scatter Plot
 to express relationships between two variables

21. Scatter Plot
 Trend Lines - Correlation

22. Income / day
No. of
families
0-500 20
500-1000 30
1000-1500 50
1500-2000 70
2000-2500 40
2500-3000 30
3000-3500 10
. .
0
10
20
30
40
50
60
70
80
0 1000 2000 3000 4000
No.of
families
Income

23. age (xi) x-xi (x-xi) sqr.
A 21 2 4
B 22 1 1
C 23 0 0
D 24 -1 1
E 25 -2 4
mean x 23 Sum 0
10 (sum x-xi sq)
Avg Sq (variance) 2 (10 by 5), n=5
SD (root v) s 1.41

24. Age Group (years) Freq. Probability
Below 20 2 2/60
20-22 28 28/60
22-24 16 16/60
24-26 10 10/60
Above 26 4 4/60
60
Mean
(x-sample,
µ-population)
23 (years)
SD (s-sample, sigma-
population)
2 (years)
Roll.
No
Age
(yr)
1 22
2 24
3 23
4 26
5 19
6 22
. .
. .
. .
. .
. .
60 22

25.  A distribution in frequencies of observations is
known – probability distribution
 Z- Normal Distribution/Test - Mean (µ), SD-
 To compare means (1 or 2 means)
 t – Distribution/Test- Mean (x), SD (s)
 To compare means (1 or 2 means)
 Chi Square Distribution / Test
 To compare sample SD with population SD
 F Test
 To compare two sample variances

26.  A freq. distribution with bell shape curve and
some known properties
 Parameters - Mean (µ), SD (sigma)
 Known properties
 68% values are within µ ± 1 SD
 95% values are within µ ± 2 SD
 99% values are within µ ± 3 SD
 95% CI = µ ± 2.SD (range)
 Lower limit µ - 2.SD
 Upper limit µ + 2.SD

27. 23
25
27
29
21
19
17

28. Example of our case
 95% CI = µ ± 2.SD
 Lower limit = µ - 2.SD, Upper limit = µ + 2.SD,
 LL = 23 - 2.2 = 19, UL = 23 + 2.2 = 27
 95% CI Range = 19-27 years
 95% of the students in the class are in the range
of 19-27 yrs
 We are 95% confident that if we randomly select
a student from the class his/her age will be
within this range (19-27 yrs)
 Reverse is Hypothesis Testing
 If mean and SD of any population is known and if
some value is given can we determine whether it
belongs to this population or distribution ?

29. 0
+0.5
+1
+1.5
-0.5
-1
-1.5

30. When Population SD is KNOWN When Population SD is UNKNOWN
Finding Probability
 Calculate z score (test statistic) of the observed
value or hypothesized value with the formula
 Determine p value associated with particular z
score at selected significance level (5%)
 P value can be seen in the tables of the particular
test
t =

32.  Two types of Hypothesis, Null - H0, Alternate - Ha

34. P Value Method
 Determine p value
 Compare with selected
alpha level (0.05)
 p ≤ 0.05 – Reject Null
 P > 0.05 – Fail to Reject
null / accept null
 This method is generally
employed by data analysis
software – Excel, SPSS
Table Value Method
 Calculate test statistic
value – Calculated TS
Value
 Determine Critical value
of test statistic at
selected significance level
– Table TS Value
 If TSCal ≥ TSTab – Reject
Null
 If TSCal < TSTab – Fail to
Reject null / accept null
 This method is generally
employed when manual
testing is done

38. RN
Gender
G
Caste
C
Age
A
Mob.No.
No. of
Classes
N
Marks
Obtained
M
Specialization
Opted
S
1 1 1 22 9450366367 87 72 HR-3
2 1 2 24 8004896712 65 68 HR-3
3 2 1 26 9934876545 48 56 Fin.-2
4 2 1 21 2542543598 95 83 Mktg.-1
5 2 3 22 9458098734 65 58 Fin.-2
6 1 1 23 9412890112 74 65 Mktg.-1
• Mean & Variance (SD) – Eg. A, N, M – sample stat. – x, s
• Correlation Eg. N-M, A-N, A-M – r
• Association between Gender and Sp. Opted (G n S) - chi
Note Sample Ch.c – Statistic , Population Ch.c - Parameter

39.  Assume a population – N, µ,
 Now assume we take many samples of size n and
calculate mean for each sample
 x1, x2, x3, x4, x5, x6, . . . . . . . . x100
 Can we make a freq. distribution of these values
and draw a curve?
 Now when we draw a distribution of these values
we will have an average (x) and SD (s)
 This average is called mean of means and
considered mean of population
 The SD of population is calculated as
which is called as Standard Error

42.  Sample mean & their difference - z / t
 Sample correlation statistic– z / t (derived from r)
 Variance (SD2) – F
 Association – Chi Sqr.
 Central Limit Theorem
 If we collect many samples and draw its
distribution the mean of this distribution is
population mean and SD of population is
 We use CLT in Hypothesis Testing

43.  z - when is Known and sample size is ≥ 30
 t - when is Unknown and sample size < 30
 In sample estimation t test is employed
 Example - H0 & H1
 H0 – There is no difference b/w mean of two groups
 H1 – There is a significant difference b/w mean of two groups
 H0 – There is no difference b/w mean marks of males &
females
 H1 – There is a significant difference b/w male & females
 Hypothesis Testing steps
 Set Null Value (u1=u2, u1-u2=0) – Make Null Distribution –
Calculate z /t sample test statistic – compare with table
value/set p value – reject/accept null

44.  Used to compare variance of two samples
 Employed in ANOVA – analysis of variance
 When there are more than two groups and their
means are to be compared
 Example
 Comparison of marks among three streams of
students arts, commerce and science
 H0 – There is no difference among mean marks of three groups
 H1 – There is a significant difference among mean marks of three
groups
 Set Null Value (µ1=µ2=µ3) – Make Null Distribution – Calculate F
test statistic – compare with table value/p value – reject/accept
null

45.  Test of Independence
 It is used to determine association between two
categorical variables (nominal & ordinal)
 Example
 Gender (M/F) and Opted Specialization (M/F/HR)
 Question like ‘is any specialisation is preferred by
females?’ are answered
 H0 – There is no association b/w gender and opted speclisa.n
 H1 – There is a significant association b/w gender & opted
speclisa.n
 Here, mean is not calculated instead frequency of categories
is taken into consideration
 Actual Frequency and Expected Frequency

46.  Cross tabs are used to calculate actual & expected freq
 Hypothesis Testing steps
 Set Null Value (actual freq. = expected freq.) – Make Null
Distribution – Calculate chi sqr. sample test statistic –
compare with table value/set p value – reject/accept null
Two Variable Interaction – Crosstab
Opted
Specialization
Total
(60)
Gender
Male (40) Female (20)
Mktg. 30 20 8
Fin. 15 10 2
HR 15 10 10
60 40 20

47.  Set Null and Alternate Hypothesis – H0 H1
 Select the null value
 Null – status quo, no difference, no effect
 Status quo – no change
 No difference – 0 difference
 No relationship – 0 effect / 0 correlation
 No association – 0 relationship (b/w nominal variab.)
 It is assumed that H0 is true in population
 Draw Null Distribution – find range of expected values
if null is true (µ ± 2.SE)
 Take observed value from sample and compare with
expected null values
 If observed value is among expected null range –
accept null
 If observed value is different from null range – reject
null

48. 1. Univariate/Bi-variate 2. Muti-variate
 Mean/Variance
Estimation
 Z test
 T test
 Chi Square
 F Test
 Correlation
 Correlation
 Regression
 Discriminant
 Cluster Analysis etc.

49.  Regression analysis
 1 dependent variable/DV (continuous)
 many independent variables/IV (continuous)
 Y = a.x1 +b.x2 +c.x3…….+.x.n
 Discriminant analysis
 1 dependent variable (catgorical)
 many independent variables (continuous)
 Z (yes/no) = a.x1 +b.x2 +c.x3…….+.x.n

50.  Cluster analysis
 No DV/IV
 Used to group respondents/customers in
various cluster
 Employed in market segmentation
 Factor analysis
 No DV/IV
 Used to group variables in various cluster of
more condensed variables