1. TABLE OF CONTENTS
iv
Chapter
# CONTENT Page
#
1 BASIC IDEAS IN STATISTICS……………………….. 01
Introduction.........................................................................
Meaning of statistics………………………………………
Applied statistics……………………………………….....
Descriptive statistics………………………………………
Inferential statistics…………………………………….....
Population…………………………………………………
Sample………………………………………………….....
Parameter………………………………………………….
Statistic……………………………………………………
Ratio………………………………………………………
Proportion…………………………………………………
Uses or importance of statistics in various fields…..……..
Constant…………………………………………...............
Variables……………………………………......................
Collection of data…………………………………….……
Collection of primary data……………………………..….
Collection of secondary data……………………………....
Grouped ungrouped data…………………………….....
Class, class interval, class boundary……………………....
Frequency (class frequency)………………………………
Class magnitude…………………………………………...
Class limit…………………………………………………
Frequency distribution/statistical series…………………...
Tabulation…………………………………………………
Classification………………………………………...........
Steps involve in the construction of classification
according to class interval (frequency distribution)…….....
Exercise…………………………………………………..
01
02
02
02
03
03
03
03
03
03
03
04
04
05
06
06
07
08
09
09
09
09
10
11
13
14
19
2 MEASURES OF CENTRAL TENDENCY……………. 21
Introduction.........................................................................
Arithmetic mean..................................................................
Merits and demerits of arithmetic mean..............................
21
22
22
2. Median.................................................................................
Merits demerits of median..............................................
Quartiles..............................................................................
Deciles.................................................................................
Percentiles...........................................................................
Mode....................................................................................
Merits demerits of mode.................................................
Exercise…………………………………………………..
v
26
26
33
34
35
42
43
49
3 MEASURES OF DISPERSION (VARIATION)……… 51
Introduction.........................................................................
Range...................................................................................
Inter quartile range..............................................................
Semi-inters quartile range (or) Quartile deviation..............
Mean deviation (or) average deviation...............................
Variance standard deviation...........................................
Variance standard deviation (by short cut method).......
Co-efficient of variation (dispersion).................................
Exercise…………………………………………………..
51
52
54
54
58
62
63
63
71
4 SIMPLE CORRELATION REGRESSION………... 73
Correlation.........................................................................
Types of correlation...........................................................
⇒ Positive correlation................................................
⇒ Negative correlation...............................................
⇒ Zero correlation......................................................
⇒ Perfect correlation...................................................
· Perfect positive correlation...........................
· Perfect negative correlation..........................
Graphic method of measuring correlation........................
Co-efficient of correlation.................................................
Rank order correlation…………………………………….
Regression………………………………………………...
Regression Equation………………………………………
Regression line…….……………………………………...
Properties of Regression line……………………………...
Exercise…………………………………………………..
73
74
74
74
74
74
75
75
75
78
87
94
94
95
95
103
3. 5 STATISTICAL INFERENCE…………………...……... 105
Introduction.........................................................................
Hypotheses………………………………………………..
⇒ Statistical hypotheses………………………………
⇒ Null hypothesis…………………………………….
⇒ Alternative hypothesis……………………………..
⇒ Simple hypothesis………………………………….
⇒ Composite hypothesis……………………………...
Type-I error and type-II error……………………………..
Level of significance……………………………………...
One tailed and two tailed tests……………………………
Test statistic……………………………………………….
Critical region and non-critical region……………………
General procedure in testing of hypothesis……………….
Test based on normal distribution………………………..
Testing hypotheses about difference between two
populations means (normal distribution)…………………
The student-t distribution…………………………………
Degree of freedom………………………………………...
Testing procedure of “t-distribution” for single
population………………………………………………..
Testing hypothesis about difference of means of two
normal populations with δ1= δ2 but unknown……………
Testing hypotheses about difference of means of two
normal populations when δ1=δ2 but unknown………….
Testing hypothesis about difference of means of two
normal populations with δ1≠δ2 but unknown……………
Testing hypotheses about difference of means of two
normal populations when δ1≠δ2 but unknown…………..
Paired difference t-test……………………………………
Testing hypotheses about two means with paired
observations………………………………………………
Exercise…………………………………………………..
vi
105
106
107
108
108
109
109
110
110
111
112
112
113
116
126
132
132
133
138
139
146
147
149
150
157
6 CHI-SQUARE (c2) DISTRIBUTION………………...... 159
Introduction.........................................................................
Testing hypotheses about variance of a normal population
Properties of chi-square (c2) distribution…………………
159
160
160
4. Testing hypotheses about variance of a normal population
c2-test for goodness of fit…………………………………
c2-test as test of independence……………………………
Contingency table…………………………………………
Exercise…………………………………………………..
vii
161
166
169
169
181
Table: Student’s t-distribution …………………………………....
Table: Area for a Standard Normal Distribution…………………
Table: Distribution of χ2……………………………………………
Glossary……………………………………………………….………
References……………………………………………………….……
183
184
185
187
195
