This presentation provide you the basics of Statistics in this wide range of different Frequencies etc. Hope you people will like it.

2. Presentation Topic:
Statistics
Teacher: Mr. Tayyab Sir
DATE:14/OCTOBER/2015
Presented by: FAZLI KHALIQ
Semester: 3rd
Department of Computer Science
AWKUM Buner Campus

3. TABULATION:
 A systematic presentation of data classified under suitable heads and sub heads and placed
in column and rows.
 A table is a rectangular arrangement of data into column and rows.
 The process of arrangement of data in tabular form is called Tabulation.
 TYPES OF TABULATION:
There are two types of Tabulation.
1)Simple Tabulation 2) Complex tabulation.
 1)Simple Tabulation:
 When data is classified according to one characteristic so then this type of Tabulation is called Simple
Tabulation.
 E.G: Marks of a student, income of a person.
 2) Complex Tabulation:
 When data is classified according to two or more characteristics then this type of Tabulation is
called Complex Tabulation.
 It is also called Double Tabulation.
 E.G: sex, weight and height etc.

4. FREQUENCY DISTRIBUTION:
 The arrangement of a set of data in a table showing form then the distribution of the data
into classes or groups together with the number of observation in each class or groups is
called frequency distribution.
 While Data is arranged & summarized in the form of a frequency distribution are often called
grouped data.
FORMATION OF FREQUENCY DISTRIBUTION:
 1) Number of classes:
 A frequency distribution should not have too few or too many large number of classes.
 The number of classes should not be greater than 25 and should not be less than 6.
 2) Class Limits:
 The class limits are two numbers which specify the classes.
 The smaller numbers is lower limit and the larger number is the upper limit.
 For example:
5 --- 10
11 ---15
 Here 5 and 11 are the lower limit and 10 and 15 are the upper limit.

5. FREQUENCY DISTRIBUTION:
 3) Class Boundaries:
 The class boundaries are the precise number which separate one class from another class.
 If one have grouped frequency distribution with class limits having between the upper class limit
of class and the lower class limit of the next class.
 We can subtract half of the length form the lower class limit and add to the upper class gap limit.
 For Example:
 11-15 the class boundaries are 10.5 – 15.5.
 4) Class Marks:
 A class mark (mid Point) is that number which divides each other into two equal parts.
 It is obtained by dividing the sum of the lower class limit and upper class limit divided by 2.
 Class Mark= (lower class limit+ upper class limit)/2.
 5) Class Intervals:
 The class interval (class width) is the difference between the upper class boundary and lower
class boundary.
 It is denoted by “h”.

6. FREQUENCY DISTRIBUTION:
 6) Class Frequency:
 The total number of observations in a class is called class frequency.
 It is denoted by “f”.
 Example:
 Weekly wages in rupees of 72 wages earns in a factory.
14,20,18,25,26,30,13,19,13,20,22,21
19,18,24,24,28,45,17,33,36,25,24,31
20,40,39,37,36,31,26,27,28,29,22,16
24,45,30,24,40,29,15,18,27,28,30,47
48,46,47,41,43,39,37,38,33,44,18,24
21,50,49,44,40,54,26,55,57,56,37,38.

7. FREQUENCY DISTRIBUTION:
Weekly wages in
rupees (class limit)
Class Boundary Tally F Class Marks
13-17 12.5-17.5 |||| | 6 (12.5+17.5)/2=15
18-22 17.5-22.5 |||| |||| ||| 13 (17.5+22.5)/2=20
23-27 22.5-27.5 |||| |||| ||| 13 (22.5+27.5)/2=25
28-32 27.5-32.5 |||| |||| 10 (27.5+32.5)/2=30
33-37 32.5-37.5 |||| || 07 (32.5+37.5)/2=35
38-42 37.5-42.5 |||| ||| 08 (37.5+42.5)/2=40
43-47 42.5-47.5 |||| ||| 08 (42.5+47.5)/2=45
48-52 47.5-52.5 ||| 03 (47.5+52.5)/2=50
52-57 52.5-57.5 |||| 04 (52.5+57.5)/2=55
Total |||| |||| |||| ||||
|||| |||| |||| ||||
|||| |||| |||| ||||
|||| |||| ||
72

8. FREQUENCY DISTRIBUTION:
 RELATIVE FREQUENCY DISTRIBUTION:
 When each class frequency is divided by the total frequency of all classes then this is known by
Relative Frequency Distribution.
 PERCENTAGE RELATIVE FREQUENCY DISTRIBUTION:
 The Percentage of each frequency can be obtained by multiplying the Relative Frequency distribution
by 100 then this will be called Percentage Relative Frequency Distribution.
 COMULATIVE FREQUENCY DISTRIBUTION:
 The cumulative form of a frequency distribution is called cumulative frequency distribution.
 The total Frequencies of various classes from the “Lowest value to the Highest value” is called
“less than type” cumulative frequency and a distribution thus obtained is called as a “less than type”
cumulative frequency distribution.

9. FREQUENCY DISTRIBUTION:
Class limit Class Boundaries F Class Mark Upper Class
Boundary
Cumulative
Frequency
Relative
C.F
Percentage
Relative C.F
40-49
50-59
60-69
70-79
80-89
90-99
100-109
39.5-49.5
49.5-59.5
59.5-69.5
69.5-79.5
79.5-89.5
89.5-99.5
99.5-109.5
1
3
4
5
4
2
1
44.5
54.5
64.5
74.5
84.5
94.5
104.5
49.5
59.5
69.5
79.5
89.5
99.5
109.5
1
4
8
13
17
19
20
1/20=0.05
4/20=0.20
8/20=0.40
13/20=0.65
17/20=0.85
19/20=0.95
20/20=01
0.05*100=5
0.2*100=20
0.4*100=40
0.65*100=65
0.85*100=85
0.95*100=95
1*100=100
20

10. DIAGRAMS & GRAPHS:
 In these methods numerical values or relationships are shown in pictorial form.
 The visual representation of data in the form of a graph or diagram is known as Graphic
Representation.
 BAR CHARTS:
 The charts are one of the most useful and commonly used techniques.
 The Bar charts consists of
 Simple Bar charts &
 Multiple Bar chart.
 1)SIMPLE BAR CHART:
o A simple bar chart consists of horizontal or vertical bars of equal width and lengths proportional
to the values they represent.
o It is useful for a linear or one bimensial comparison.

11. DIAGRAMS & GRAPHS:
0
1
2
3
4
5
6
44.5 54.5 64.5 74.5 84.5 94.5 104.5
Simple Bar Chart
Class Boundary

12. DIAGRAMS & GRAPHS:
 2)MULTIPLE BAR CHART:
o A diagram that compares two or more characteristics at a time is called Multiple Bar charts.
o Example:
• Represent the following data in a Multiple Bar Chart.
Sol: We will adjust the data by tour groups of bar having three adjacent bars representing
the price for export in Cotton, Rice and Sugar.
Year Cotton Rice Sugar
1998 100 45 22
1999 175 63 30
2000 250 120 55
2001 325 175 100

13. DIAGRAMS & GRAPHS:
0
50
100
150
200
250
300
350
1998 1999 2000 2001
Multiple Bar Chart
Cotton Rice Sugar2

14. DIAGRAMS & GRAPHS:
 FREQUENCY POLYGON:
 When class frequencies are plotted against corresponding class marks the graph is called a
Frequency Polygon.
44.5, 1
54.5, 3
64.5, 4
74.5, 5
84.5, 4
94.5, 2
104.5, 1
0
1
2
3
4
5
6
44.5 54.5 64.5 74.5 84.5 94.5 104.5
Frequency Polygon
Class Mark

15. DIAGRAMS & GRAPHS:
 SUB-DIVIDED BAR DIAGRAMS:
 It is a set of different colored bars representing the total as a whole and then further divided
according to the parts or components.
55
110
200
300
35
70
115
175
20
25
75
50
25
35
60
40
0
100
200
300
400
500
600
1985 1986 1987 1988
Sub-Divided Bar Chart
Agriculture Health Industry Education

16. DIAGRAMS & GRAPHS:
 PIE-CHARTS:
 A Pie Charts is a graphic device consist of a circle divided into sectors whose areas are proportional
to the various parts into which the whole quantity is divided.
 Example:
 Show the population of provinces and FATA and construct a pie chart to compare population.
Name Population (In
Million)
Sindh
KPK
Balochistan
FATA
Punjab
26
23
8
4
65
Total 126

17. DIAGRAMS & GRAPHS:
 Total Population= 26 Millions
o Angle=quantity/total quantity*360
o For Sindh=26/126*360=74.3◦
o For KPK=23/126*360=63.7◦
o For Balochistan=8/126*360=23◦
o For FATA=4/126*360=11◦
o For Punjab=65/126*360=185.71◦
Punjab
52%
Sindh
21%
KPK
18%
Balochistan
6%
FATA
3%
Population
Punjab
Sindh
KPK
Balochistan
FATA

18. THANK YOU