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Organisation of Data

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Topics

description

  • Ungrouped Data
  • Grouped Data

definition

Unorganised/Raw data: Unorganised form of data is called raw data.

Grouped data: Grouped data means observations are classified into groups.

Frequency: Frequency gives the number of times that a particular entry occurs.

Frequency tables: A frequency table shows the list of categories or groups of things, together with the number of times the items occur.

Class Interval: While arranging a large amount of data in statistics, they are grouped into different classes to get an idea of the distribution, and the range of such class of data is called the Class Interval.

Upper Limit: In each class interval, the greatest number is the upper-class limit.

Lower Limit: In each class interval, the smallest number is the lower class limit.

Class Size: This difference between the upper-class limit and lower class limit for each of the class intervals is equal is called the width or size of the class interval.

Class Mark: The midpoint of each class interval is the class mark.

Class Mark = `"Upper Limit + Lower limit"/2`.

Tally Mark: Tally Mark refers to a group of five marks that should be used as a cross, as shown by `cancel(||||}`. They are tally marks.

formula

Class Mark = `"Upper Limit + Lower limit"/2`.

notes

Organisation Data:

  • To draw meaningful inferences, we need to organize the data systematically.

  • The data that is collected needs to be organized in a proper table so that it becomes easy to understand and interpret.

A. Ungrouped Data:

  • Data mostly available to us is in an unorganized form called raw data.

  • The observations are not classified into groups.

Consider the following example,

1) Ms. Neelam, class teacher wanted to find how children had performed in English. She writes down the marks obtained by the students in the following way:

23, 35, 48, 30, 25, 46, 13, 27, 32, 38

In this form, the data was not easy to understand. She also did not know whether her impression of the students matched their performance.

Neelam’s colleague helped her organise the data in the following way

Roll No.

Names

Marks out of 50

Roll No.

Names

Marks out of 50

1

Ajay

23

6

Govind

46

2

Armaan

35

7

Jay

13

3

Ashish

48

8

Kavita

27

4

Dipti

30

9

Manisha

32

5

Faizaan

25

10

Neeraj

38

In this form, Neelam was able to know which student has got how many marks. But she wanted more. Deepika suggested another way to organise this data.

Roll No.

Names

Marks out of 50

Roll No.

Names

Marks out of 50

3

Ashish

48

4

Dipti

30

6

Govind

46

8

Kavita

27

10

Neeraj

38

5

Faizaan

25

2

Armaan

35

1

Ajay

23

9

Manisha

32

7

Jay

13

Consider another example:

2) A group of students was asked about their favourite subject. The results were as listed below:

Art, Mathematics, Science, English, Mathematics, Art, English, Mathematics, English,

Art, Science, Art, Science, Science, Mathematics, Art, English, Art, Science, Mathematics, Science, Art.

Which is the most liked subject and the one least liked?

⇒ It is not easy to answer the question looking at the choices written haphazardly.

We arrange the data using tally marks.

Subject Tally Marks Number of Students
Art `cancel(||||)` || 7
Mathematics `cancel(||||)` 5
Science `cancel(||||)` | 6
English |||| 4

The number of tallies before each subject gives the number of students who like that particular subject. This is known as the frequency of that subject.

  • Frequency: Frequency gives the number of times that a particular entry occurs.

  • Frequency tables: A frequency table shows the list of categories or groups of things, together with the number of times the items occur.

B. Grouped Data:

  • In grouped data, observations are classified into groups.

  • For example, a class of students got different marks in a midterm exam. The data is tabulated as follows:

Mark Interval

0-20

21-40

41-60

61-80

81-100

No. of Students

8

14

45

39

8

  • This shows how many students got a particular mark range. Grouped data is easier to work with when a large number of data is given.

Class interval related concept:

Class Interval: While arranging a large amount of data in statistics, they are grouped into different classes to get an idea of the distribution, and the range of such class of data is called the Class Interval.

Upper Limit: In each class interval, the greatest number is the upper-class limit.

Lower Limit: In each class interval, the smallest number is the lower class limit.

Class Size: This difference between the upper-class limit and lower class limit for each of the class intervals is equal is called the width or size of the class interval.

Class Mark: The midpoint of each class interval is the class mark.

Class Mark = `"Upper Limit + Lower limit"/2`.

Tally Mark: Tally Mark refers to a group of five marks that should be used as a cross, as shown by `cancel(||||}`. They are tally marks.

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