1. Chapter 2 Organizing Data
Nutan s. Mishra
11/22/2018
University of South Alabama

2. University of South Alabama
Raw Data
A data recorded in the form as it was collected without ranking or processing is called raw data.
Example: consider the status of following 20 students. The four status are SO, F, J, SE
This also called
ungrouped data. J F SO SE
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University of South Alabama

3. University of South Alabama
Grouped Data
Status x
# of students
(frequency f) F 6 SO 4 J SE
This is categorical (qualitative) data
x= status
f= frequency
The data set consist of 20 members. The sum of frequencies of all the categories is equal to size of the data set .
i.e. Σf = f1 + f2 + f3 + f4 = 20
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University of South Alabama

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Relative frequency
Status x
# of students
(frequency f)
Relative frequency
Percentage F 6
6/20
(6/20)*100 SO 4
4/20
(4/20)*100 J SE
Relative frequency of a category =
frequency of that category/ sum of all frequencies
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University of South Alabama

5. Graphical presentation
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University of South Alabama

6. Organizing Data (quantitative)
Consider the following table
This is the organized data for the quantitative variable GPA. The table shows that there are 10 students whose GPA falls between 0 and 1 and …
The values of x are divided into four distinct classes. Each class is an interval of values.
GPA (x)
Number of Students (f)
0 to 1 10
1 to 2 34
2 to 3 40
3 to 4 16
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University of South Alabama

7. Organizing Data (quantitative)
This is called Frequency Distribution Table or just frequency distribution .
Class width = upper boundary-lower boundary
Class midpoint =
(upper boundary+lower boundary)/2
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University of South Alabama

8. Construction of frequency distribution
That is how to divide data into classes?
How many classes?
Depends on size of the data set. Vary between 5 and 20.
What should be the class width?
Approximately
(largest value-smallest value)/number of classes
11/22/2018
University of South Alabama

9. Example of classification
Consider the following raw data on GPA of 30 students.
We know that the variable GPA =x varies between 0 and 4
Number of classes can be 3 or 4 or 5. let it be 3
Then class width = ( )/3 =
1.68
2.35
2.59
3.99
2.87
3.23
3.78
2.00
2.74
1.54
2.15
3.22
1.78
3.66
3.01
3.27
2.55
2.29
3.39
3.94
3.00
2.75
1.77
1.99
3.45
2.28
3.07
11/22/2018
University of South Alabama

10. Example of classification
And the frequency table is as follows
Relative frequency of a class
= frequency of that class/ sum of all frequencies
= f/Σf x f
r.f.
percent
1 to 2 5
5/30
(5/30)*100= 16.67
2 to 3 12
12/30
(12/30)*100= 40
3 to 4 13
13/30
(13/30)*100= 43.33
11/22/2018
University of South Alabama

11. Important note about classification
Most of the statistical software accept only raw data as input and they classify data for us.
Thus if we are using a software to analyze our data, we do not have to worry about the classification part.
Software gives us ability to change the number and width of the classes according to the need of the problem.
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University of South Alabama

12. Cumulative frequency distribution
A cumulative frequency distribution gives the total number of values that fall below the upper boundary of each class.
Example: Application 2.34 from the textbook frequency cumulative frequency
Number of Checks
Number of students
0 to 99 39
100 to 199 21
200 to 299 18
300 to 399 15
400 to 499 7
Number of Checks
Number of students
0 to 99 39
0 to 199 60
0 to 299 78
0 to 399 93
0 to 499
100
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University of South Alabama

13. University of South Alabama
Frequency Curve
Number of Checks
Modified classes
Midpoint of class
Number of students
0 to 99
0 1o 100 50 39
100 to 199
100 to 200
150 21
200 to 299
200 to 300
250 18
300 to 399
300 to 400
350 15
400 to 499
400 to 500
450 7
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University of South Alabama

14. Ogive (Cumulative frequency curve)
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University of South Alabama

15. University of South Alabama
Stem and Leaf display
A way of organizing and display quantitative data. Each value is divided into two parts – a stem and a leaf. \
To draw a stem-n-leaf plot its helpful to know the range of the data that is max value and min value
If can not find out exact values of max and min, the approximate value can given us some idea about the range of the data.
Consider the following data set of scores of 30 students in Statistics exam 75 52 80 96 65 79 71 87 93 95 69 72 81 61 76 86 68 50 92 83 84 77 64 57 98
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University of South Alabama

16. Stem and leaf display
In this data set the values range between 50’s and 90’s.
Thus we would like to count the number of values in 50’s, in 60’s in 70’s and so on
That we declare the tenth place as stem and unit place as a leaf.
Thus the resulting stem and leaf plot is as follows:
Stem
leaves
Leaves arranged in order 5
2 0 7
0 2 7 6 7 8 9
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University of South Alabama