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| Image credit: Pixabay.com |
Data
Qualitative Data & Quantitative Data
Qualitative data provide descriptive information of a observation. Data are categorised according to physical traits, gender, colors or anything that does not have a number associated with it.Quantitative data provide numerical information of a observation.
➧ We would consider Quantitative data (Numerical data).
➧ It must be collected appropriately.
➧ e.g Data of cricket match would consist of numbers of run scored, numbers of over bowled etc whereas data of exam would consist of marks obtained by different students in a class. Similarly data of lipe span of people in a country would consist of ages of people in that country .
Raw Data & Organised Data
Unorganised data is called raw data. They are often large and difficult to analyse.Systematically classified and arranged data which can be analysed and interpreted is called organised data.
Organising / Representing Data
The collected data need to be organised in a proper order or groups if large.The organised data is then represented through a table or a graph.
Tabulation or Tubular form of Data
In tubular form, data is arranged in columns and rows.It can be of following types:
➢ Tally chart
➢ Frequency Distribution Table
➢ Group Frequency Distribution Table
Tally marks
It is a easy and fast way of keeping track of number in counting or tallying ongoing result.
In tally charts numerical data is represented by tally marks in a table.
(Ex-9.1)Q1.
In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.8 1 3 7 6 5 5 4 4 2
4 9 5 3 7 1 6 5 2 7
7 3 8 4 2 8 9 5 8 6
7 4 5 6 9 6 4 4 6 6
(a) Find how many students obtained marks equal to or more than 7.
(b) How many students obtained marks below 4?
Ans.
| Marks Obtained | Tally Marks |
| 1 2 3 4 5 6 7 8 9 |
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(a). 12 students obtained marks equal to or more than 7.
(b). 7 students obtained marks below 4.
Frequency
How many times a particular value occur in a data is called its frequency e.g., in above example frequency of 1 mark is 2, frequency of 2 marks is 3, frequency of 3 marks is 3 and so on.FDT
When we arrange data variables and their frequency in the form of table, it is called frequency distribution table.It is same like tally charts where we use tally marks instead of numbers to show the frequencies.
We can use both tally marks and numbers to show the frequency in frequency distribution table.
Frequency distribution table for the earlier example ↴
| Marks Obtained | Tally Marks | Frequency |
| 1 2 3 4 5 6 7 8 9 |
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| 2 3 3 7 6 7 5 4 3 |
We can add up the frequencies to check our result.
Grouping Data | ↓Class 8 |
Data presented in this manner is said to be grouped and the distribution obtained is called grouped frequency distribution.
Grouped Frequency Distribution Table
Groups
|
Tally Marks
|
Frequency
|
0−10
|  |
3
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10−20
|  |
9
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20−30
|  |
19
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30−40
|  |
15
|
40−50
|  |
4
|
Total
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50
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e.g., following is the grouped frequency distribution table of marks (out of 50) obtained in Mathematics by 50 students .
21, 10, 30, 22, 05, 37, 12, 25, 15, 39, 26, 32, 18, 27, 28, 08, 29, 35, 31, 24, 18, 20, 38, 22, 16, 24, 10, 27, 28, 49, 29, 32, 23, 31, 21, 34, 23, 36, 36, 47, 48, 39, 20, 07, 16, 36, 47, 30, 22, 17.
Group/Class Interval
Each of the groups (0-10, 10-20, 20-30, etc.,) in group frequency distribution table is called a Class Interval (or briefly a class).Upper Class Limit & Lower Class Limit
Upper limit of the class interval is called Upper class limit and lower limit of the class interval is called Lower class limit.e.g., In group 0−10, 0 is the lower class limit and 10 is the upper class limit.
The common observation belongs to the higher class, i.e., 10 belongs to the class interval 10-20 (and not to 0-10).