INSTRACTOr:
BILAL KHAN
MBA(MARKETING)Msc(Economics)
MIHE:
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Series 1
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accounts
accounts
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Introduction to business Statistics.
Chapter No 01
What is statistics?
 Numerical data relating to an aggregate of individuals, the
science of collecting, analyzing and interpreting data is called
statistics.
Conti…
Height(ft)
Weights(kg)
No. of students
4.2
45-49
1
4.5
50-54
4
4.7
55-59
17
6
60-64
28
5.5
65-69
25
5
70-74
18
5.8
75-79
13
Importance of statistics in Business.
 Statistics play an important role in business, because provides
a quantitative basis for arriving at decisions in all matters
connected with operating of business.
 For example producers must know the demand of his
consumers.
 Statistics would help to plan production according to the
demands of consumers
Conti…………
 The banks make use of statistics while framing their policies.
The banks have to conduct constant enquiries regularly
deposits under different categories, the nature of demand for
daily with-drawls etc.
Difference between Parameter and
statistic.
 Parameter.
A number that describes some property of a
population is called parameter
 For example a numerical value such as mean and mode
etc…..

Conti………
 Statistic.
A number that describes some property of a sample
is called statistic.
 For example the average length calculated for a random(hit
and miss) sample of a college students.

Difference between population and
sample.
 Population.
The aggregate or totality of all the individual
items about which information is required is called
population
 For example if 1000 students in the college that we classified
according to blood type.

Conti…….
 Sampling.

The study of observing the single part or only a part
of the population , such a part is called sampling.
Difference between Descriptive and
inferential statistics.
 Descriptive statistics.
Those statistics method which is
concerned with collecting and describing a set of data so as
to yield meaningful information.
 For example teacher computes an average grade for his
statistics class. The average grade describes the performance
of that particular class.

Coati…..
 Inferential statistics.
Those statistics methods which is
concerned with the analyzing of a subset of a data leading to
inference about the entire set of a data.
 For example the academic records of the metric classes
during the past five years at a nearby government school
show that 45% of the entering freshmen eventually
matriculated.

What is variable.
 A quantity which may take any one of a specified set of
values.
 For example the height of a students, rainfall at a place, price
of a commodity etc.
Discrete Variable.
 A discrete variable can assume only a finite number.
 For example the number of children in a family, the number
of goals scored by a player etc.
Continuous variable
 A continuous variable may take an infinite number of values
between any two points such as the height of a student, the
temperature at a place etc.
Quantitative variable.
 If the values are expressed numerically the variable is said to
be quantitative.
 Foe example age, weight, income, number of children etc.
Qualitative variable.
 If the values are not expressed in the numerical form is called
qualitative variable.
 For example smoking, poverty intelligence etc.
Chapter no 2
 Collection




and
Presentation
Of data.
What do you mean by classification.
 Classification.
It is the process of arranging data into
sequences and groups according to their common
characteristics.
 For example we may arrange the marks into group of 60
marks each like 01 to 59, 60 t0 119 etc.

Conti..
Weights(kg)
No. of students
45-49
1
50-54
4
55-59
17
60-64
28
65-69
25
70-74
18
75-79
13
Types of classification:
 1: Descriptive
 2:Numerical.
Descriptive classification:
 When the data are classified on the basis of quality which are







incapable of quantitative measurement the classification is said to
be descriptive.
For example classification according to the sex and marital status
divide the population into six classes.
Male married
Male unmarried
Male widowed
Female married
Female unmarried
Female widowed
Numerical Classification
 This type of classification is applicable to quantitative data
only.
 For example data related to the height, weight, income and
production etc.
What do you mean by tabulation of
statistical data
 Tabulation simply means presenting of data through tables.
 It is the next of classification in the process of statistical
investigation.
 To be more precise tabulation is an orderly arrangement of
data into columns and rows.
Conti….
Classes
Class boundaries'
Mid points
Tally
Frequency
65-84
64.5-84.5
74.5
//// ////
9
85-104
84.5-104.5
94.5
105-124
104.5-124.5
114.5
//// //// //// //
17
125-144
124.5-144.5
134.5
//// ////
10
145-164
144.5-164.5
154.5
////
5
165-184
164.5-184.5
174.5
////
4
185-204
184.5-205.5
194.5
////
5
//// ////
10
Simple tabulation
 A simple tabulation contains data regarding one
characteristics only.
 Information relating to the other characteristics being
ignored.
Conti…
Weights(kg)
No. of students
45-49
1
50-54
4
55-59
17
60-64
28
65-69
25
70-74
18
75-79
13
Complex tabulation
 Shows the division of the data into two or more categories:
Height(ft)
Weights(kg)
No. of students
4.2
45-49
1
4.5
50-54
4
4.7
55-59
17
6
60-64
28
5.5
65-69
25
5
70-74
18
5.8
75-79
13
Distribution…
 Arrangement of data according to the values of a variable
characteristics is called distribution
Years
Population(In Millions)
1998 1999 2000 2001 2002
40
45
60
64
68
Conti…
Year
Imports
exports
1992-1993
8
4
1993-1994
10
6
1994-1995
12
9
1995-1996
18
13
1996-1997
20
17
What is frequency distribution?
 A large mass of data possessing different characteristics is
grouped into different classes.
 The observation are determined in each class.
 The arrangement of these classes into tabular form makes
frequency distribution.
Conti…..
Class limit
Tally
Frequency
Class boundaries
48.6-53.5
/
1
48.55-53.55
53.6-58.5
//
2
53.55-58.55
58.6-63.5
/
1
58.55-63.55
63.6-68.5
////
4
63.55-68.55
68.6-73.5
//// ///
8
68.55-73.55
73.6-78.5
////
5
73.55-78.55
78.6-83.5
//// ///
8
78.55-83.55
83.6-88.5
/
1
83.55-88.55
88.6-93.5
/
1
88.55-93.55
93.6-98.5
/
1
93.55-98.55
32
Class frequency and grouped data
 The number of observation falling in a class makes a class
frequency.
 Data organized and summarized in the form of frequency
distribution are called grouped data.
Main points of preparing a frequency
distribution
 Number classes and their lengths
 Class-Limit
 Class boundaries
 Class-Marks or Mid point
 Class frequency
Number of classes and their lengths
 A frequency distribution should not have too few or too
many large.
 Depending upon a particular data.
 The number of classes should not exceed 25 and should not
be less than 6.
Class Limit
 The limit of the class should be so fixed that the mid point of
each class interval fall on an integer and not a fraction
Class boundaries
 If one have grouped frequency distribution with class limit
having a gap between the upper class limit of one class and
the lower class limit of the next class
Class-Marks or Mid point
 Formula : lower class + upper class

2
Class frequency
 The frequency of a class interval is the total number of items
falling in that class interval
 Also called class tally sheet
 Usually after every four lines in a class the fifth item is
marked by horizontal or slanted lines across the strokes
Q : make a group frequency distribution from the following data .
 106 107 76 82 109 107 115 93 95 123 125
 111 92 86 70 126 68 130 129 139 119 115
 128 100 186 84 99 113 204 111 141 136 123 90 115
 98 110 78 185 162 178 140 112 173 146 158 194
 148 90 107 181 131 75 184 104 110 80 118 82.
 By scanning the data we find that the largest weight is 204 and the lowest is 68
so the range is 204-68=136
 Decide on the number of classes into which the data are to be grouped we used
H.A Sturges rule.
 K= 1+3.3logN.
 Where k denotes the number of classes and N is the total number of
observation.
Conti….
 Frequency distribution.
Classes
Class boundaries'
Mid points
Tally
Frequency
65-84
64.5-84.5
74.5
//// ////
9
85-104
84.5-104.5
94.5
105-124
104.5-124.5
114.5
//// //// //// //
17
125-144
124.5-144.5
134.5
//// ////
10
145-164
144.5-164.5
154.5
////
5
165-184
164.5-184.5
174.5
////
4
185-204
184.5-205.5
194.5
////
5
//// ////
10
Q: arrange the data given below in an array and construct a frequency
distribution using a class interval of 5 indicate the class boundaries
and class limit clearly
 79.4, 71.6, 95.5, 73, 74.2, 81.8, 90.6, 55.9, 75.2, 81.9,





68.9, 74.2, 80.7, 65.7, 67.6, 82.9, 88.1, 77.8, 69.4, 83.2,
82.7, 73.8, 64.2, 63.9, 58.3, 48.6, 83.5, 70.8, 72.1, 71.9,
59.4, 77.6
Ans: the value of variate range from 48.6 to 95.5. we take
class interval of length 5.
No. of classes =
range
class interval
95.5 – 48.6 = 9.38 = 10
5
Cont….
Class limit
Tally
Frequency
Class boundaries
48.6-53.5
/
1
48.55-53.55
53.6-58.5
//
2
53.55-58.55
58.6-63.5
/
1
58.55-63.55
63.6-68.5
////
4
63.55-68.55
68.6-73.5
//// ///
8
68.55-73.55
73.6-78.5
////
5
73.55-78.55
78.6-83.5
//// ///
8
78.55-83.55
83.6-88.5
/
1
83.55-88.55
88.6-93.5
/
1
88.55-93.55
93.6-98.5
/
1
93.55-98.55
32
What is simple bar chart:
 The simple bar chart is particularly appropriate for a linear
or one dimension comparison. The scale for construction of
simple bar chart should be such as facilitates the
representation of largest bar quite conveniently.
Conti….
Years
Population(In Millions)
1998 1999 2000 2001 2002
40
45
60
64
68
Chart….
80
60
40
20
0
1998
1999
2000
2001
2002
Multiple bar chart
 In this type of chart we represent two or more than two sets
of a data in one chart than more than one chart is used.
 This can be explained with the help of example, the
following table give the imports and exports of Pakistan for
year 1992 to1997.
Conti…..
Year
Imports
exports
1992-1993
8
4
1993-1994
10
6
1994-1995
12
9
1995-1996
18
13
1996-1997
20
17
Chart….
25
20
15
Imports
Exports
10
5
0
1992-93
1993-94
1994-95
1995-96
1996-97
Subdivided bar charts.
 Subdivided bar are used to present such data which are to be
shown in parts, or which are the totals of various
subdivisions. The components parts are shaded or colored
differently so as to distinguish different parts

Conti…
 For example if we want to present the development in the
field of industry, transports, and agricultural for Pakistan ,
we will draw bars with lengths proportional to the total
populations.
Conti….
Years
Indus2001try
Transports
agricultural
Total
1998
100
80
40
220
1999
120
100
50
270
2000
130
120
55
305
Chart…..
350
300
250
200
Agriculture
Transport
Industry
150
100
50
0
1998
1999
2000
Pie charts.
 The reason for the popularity of pie chart is the easiness and
convenience in its constructions. It is also known as a circle chart.
The procedure is very simple take the total of these quantities equal
to an angle of 360 degree and than convert the quantities in terms of
angles using the following formula.

angle = Quantity X 360

Total
Conti….
 This can be explained with the help of example which is
clear from the following table that shows the population of
provinces.
Name
Population in millions
Kabul
26
Jalalabad
23
wardak
8
Qandahar
4
Helmand
65
Conti….
 The corresponding angles needed to draw the the chart are
given below.
Names
Population in
millions
Angles of sector
Kabul
26
26/126x360=74.3
Jalalabad
23
23/126x360=65.7
Wardak
8
8/126x360=23
Qandahar
4
4/126x360=11
Helmend
65
65/126x360=126
Chart….
Sales
Kabul
Helmand
Qandahar
Jalalabad
Wardak
Kabul
Jalalabad
Wardak
Qandahar
Helemend
Histogram.
 When the class-boundaries are marked along the x-axis and
rectangle are constructed width proportional to class
interval size and heights proportional to class frequencies.
The resulting graph will be called a histogram.
Continue…..
Class
limits
40-49
50-59
64540-69
70-79
80-89
90-99
100-109
Frequency
1
3
4
5
4
2
1
Chart….
5
F y
r 4
e
q 3
u 2
e
n 1
c
0
39.5
49.5
59.5
69.5
79.5
Class Boundries
89.5
99.5
109.5
Frequency Polygon
 A frequency polygon is the geometric shape obtained by
connecting with straight lines .The mid point of adjacent
intervals of a histogram. Following figure shows the
frequency polygon .
Continue:
Class
limits
40-49
50-59
60-69
70-79
80-89
90-99
100-109
Class marks
44.5
54.5
64.5
74.5
84.5
94.5
104.5
Frequency
1
3
4
5
4
2
1
Chart:
Frequency
6
5
4
3
Frequency
2
1
0
44.5 54.5 64.5 74.5 84.5 94.5 104.5
chapter No 03

 \Measures of central tendency or averages:
Central Tendency:
 The tendency of observation to cluster in the central part of
the data set is called central tendency.
 As central tendency indicates the location or general position
of the data in the observation is called measure of location or
position.
 Location are generally known as Averages.
Types of Averages:
 The most common types of averages are:
 (1) The arithmetic Mean.
 (2) The Geometric Mean.
 (3) The Harmonic Mean.
 (4) The Median.
 (5) The Mode.
Arithmetic Mean:
 It is defined as the value obtained by dividing the sum of all
the observations by their number.
Mean = Sum of all observations

Number of observations
Population Mean:
 If the given set of observations represents a population than
the mean is called as population mean, which is usually
represented by u(mu) .
Sample mean:
 If the given set of observations represents a sample, than the
mean is called as sample mean.
 Sample mean is represented by x by putting a bar over it.
Q:The marks obtained by 9 students are given below
calculate the arithmetic mean.
 45,32,37,46,39,36,41,48,36.
 The mean is given by.
 X = 45+32+37+46+39+36+41+48+36
09
X = 360 =40 marks.

09
Q= The mean heights and the number of students in three
sections of a statistics class are given below.
Section
Number of boys
Mean height
A
40
62
B
37
58
C
43
61
Conti….
 Find the overall mean height of 120 boys:n1=40, n2=37,
n3= 43 and
 X1 = 62, X2 = 58,X3 = 61
 X =

n1X2+n2X2+n3X3
n1+n2+n3
Conti……

 (40x62) +(37x58) +(43x61)

40 + 37 + 43


7249

120
= 60.4 Ans
Mean from group data:
 When the data is very large the data are organized into a
frequency distribution.
 Formula:
 X

= f1X1 + f2X2 + ……fkXk
f1 + f2 + ………….fk