1. Methods of presenting Data
Tabular Method
Graphical Method

2. Quantitative Data Presentation
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Quantitative Data Presentation
Quantitative
Data
Ordered
Frequency
Array
Distributions
Histogram
Polygon
Ogive

3. Data Array Example smallest to largest (or largest to smallest)
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Data Array
Data placed in rank order
smallest to largest (or largest to smallest)
Example
Data in raw form (as collected)
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Data in ordered array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Information before it is arranged and analyzed is called raw data. It is called raw because it is unprocessed by statistical methods.

4. Presenting Data in Array: An Example
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Presenting Data in Array: An Example
Raw Data: Yards Produced by 30 Carpet Looms
Data are not necessarily information and having more data doesn’t necessarily produce better decisions. The goal is to summarize and present data in useful ways to support prompt and effective decisions. The reason we have to organize the data is to see whether there are patterns in them, patterns such as the largest and smallest values, and what values the data seem to cluster around.
Arrange the data in order array

5. Frequency Distribution
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Frequency Distribution
The table that organizes the data into mutually exclusive classes or categories is called frequency distribution.
One way we can compress data is to use a frequency table or a frequency distribution

6. Frequency distribution
Data in raw form
24, 24, 21, 27, 27, 30, 38, 27
Observations
Frequency 21 1 24 2 27 3 30 38

7. Frequency Distribution
Prices of books sold yesterday at bookshop:
27, 12, 13, 21, 43, 24, 37, 26, 27, 30, 17, 32, 35, 38, 41, 53, 44, 46, 24, 58.
Classes
Frequency
10 but less than 20 3
20 but less than 30 6
30 – 40 5
40 – 50 4
50 – 60 2

8. Constructing a Frequency Distribution
Determination of Range,
R = Highest value- lowest value
Determination of number of class.
H.G. Struges, K = logN
Determination of class interval, R/K
Identify the data for each class by tally mark.
Counting tally marks and frequency determination .,

9. Frequency Distribution
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Frequency Distribution
Prices of books sold yesterday at bookshop:
27, 12, 13, 21, 43, 37, 26, 27, 30, 17, 32, 35, 38, 41, 53, 44, 46, 24, 58.
Classes
Tally
Frequency
10 but less than 20 3
20 but less than 30 6
30 – 40 5
40 – 50 4
50 – 60 2
Total 20

10. Construct a frequency distribution
Marks in Business Statistics of BBA students are given below:
45,76, 89, 40, 54, 59, 62, 26, 47, 65, 78, 71, 82, 35, 45, 58, 67, 73, 72, 85, 52, 60, 67, 22, 48,50, 38, 57, 65, 78, 76, 73,68, 64, 55.
Construct a frequency distribution.

11. Some definitions Class
In process of constructing frequency distribution, raw data are assigned to some chosen groups of appropriate size. These groups are called classes.
For example
10 -20, , etc are classes.

12. Some definitions Frequency
The number of observations or values falling into each group or class is called class frequency or frequency.
For example,
5 observations fall in class 30 – 40. So The frequency of that class is 5.

13. Some definitions Class limits
Each class is formed by two boundary values. These two values are known as class limits. The smallest value is called lower limit and the upper limit is called upper limit.
For example,
For a class 30 – 40, 30 is the lower limit and 40 is the upper limit.

14. Some definitions Class-width
The size of class is referred to as the class width and is the difference between the two class limits.
For example,
Here the class width is 10.

15. Some definitions Mid- value
The value which lies in the middle of a class is called mid- value of that class.
For example
For class 30 – 40, the mid value is 35. It is obtained by (30+40)/2=35. For class 50 – 60, the mid value is 55.

16. Frequency Distribution
Classes
Frequency
10 but less than 20 3
20 but less than 30 6
30 – 40 5
40 – 50 4
50 – 60 2 16

17. Relative Frequency Distribution
The frequency distribution which presents frequencies in terms of fraction or percentage in each class is called relative frequency distribution.
Classes
frequency
Relative frequency
10 but less than 20 3
3/20= (15%)
20 – 30 6
6/20= (30%) 5
5/20= (25%)
40 – 50 4
4/20= (20%) 2
2/20= (10%)
Total 20

18. Cumulative Frequency Distribution
Cumulative frequency distribution is one which used to determine how many or what proportion of the data values are below or above a certain value.
Classes
Frequency
Cumulative frequency
% cumulative
frequency
10 but less than 20 3
15% (3/20)
20 – 30 6
9 (3+6)
45% (9/20)
30 – 40 5
14 (3+6+5)
70%
40 – 50 4
18 (14+4)
90%
50 – 60 2
20 (18 +2)
100%
Total 20

19. Data Array 1. Organizes data to focus on major features
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Data Array
1. Organizes data to focus on major features
2. Data placed in rank order
smallest to largest (or largest to smallest)
3. Data in raw form (as collected)
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
4. Data in ordered array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Information before it is arranged and analyzed is called raw data. It is called raw because it is unprocessed by statistical methods.

20. Presenting Data in Array: An Example
4/25/2017
Presenting Data in Array: An Example
Raw Data: Yards Produced by 30 Carpet Looms
Data are not necessarily information and having more data doesn’t necessarily produce better decisions. The goal is to summarize and present data in useful ways to support prompt and effective decisions. The reason we have to organize the data is to see whether there are patterns in them, patterns such as the largest and smallest values, and what values the data seem to cluster around.
Data Array:
Daily Production in Yards of 30 Carpet Looms

21. Constructing an Ungrouped Frequency Distribution
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Constructing an Ungrouped Frequency Distribution
Raw Data:
Class _
15.2
15.3
15.4
15.5
15.6
15.7
Tallies _ //
////
//// //// /
//// /
///
Frequency _ 2 5 11 6 3 30
Relative Frequency
0.07
0.16
0.37
0.20
0.10
1.00
Cumulative
Rel. Freq.
0.07
0.23
0.60
0.80
0.90
1.00
Frequency
Distribution