Representation of Data
Collection A (shown below) represents the marks obtained by 50 students in a test of 100 marks.
Collection A
80, 70, 0, 20, 20, 45, 50, 65, 30, 50, 70, 20, 4, 90, 49, 40, 45, 30, 30, 50, 20, 80, 39, 30, 50, 50, 70, 70, 20, 40, 90, 30, 40, 50, 65, 45, 70, 79, 20, 4, 30, 50, 20, 45, 50, 45, 90, 30, 4, 50
In the collection above, 80, 70, etc., are called the terms of the collection.
Depending on the form of expression, data may be raw (i.e., ungrouped) or arrayed.
I. Raw Data: The data in Collection A have been expressed as they were collected. Such data are called raw data.
But with data in raw form, computation, analysis and interpretation become difficult. Therefore, it is necessary to arrange raw data in a systematic order.
II. Arrayed Data: Data arranged in ascending or descending order are called arrayed data. The arrayed form (in ascending order) of raw data in collection A can be expressed as shown ahead.
4, 4, 4, 20, 20, 20, 20, 20, 20, 20, 30, 30, 30, 30, 30, 30, 30, 39, 40, 40, 40, 45, 45, 45, 45, 45, 49, 50, 50, 50, 50, 50, 50, 50, 50, 50, 65, 65, 70, 70, 70, 70, 70, 79, 80, 80, 90, 90, 90, 90.
Table A
|
Marks Obtained 4 20 30 39 40 45 49 50 65 70 79 80 90 Total |
Number of Students 3 7 7 1 3 5 1 9 2 5 1 2 4 50 |
Such a table helps us answer a number of questions about the performance of the students in the test. For example:
(i) What were the lowest and the height marks obtained in the test?
Answer: The lowest mark = 4 and the highest mark = 90.
(ii) How many students of obtained the highest mark in the test?
Answer: 4 students.
(iii) How many students obtained 65 marks in the test?
Answer: 2 students
(iv) What was the mark secured by the largest number of students in the test?
Answer: 50 mark.
III. Grouped Data: The data displayed in table A can be arranged in a shorter form by grouping the whole collection as shown below
Table B
|
Marks Obtained From 0 to under 20 From 20 to under 40 From 40 to under 60 From 60 to under 80 From 80 to under 100 |
Number of Students 3 15 (i.e., 7 + 7 + 1) 18 (i.e., 3 + 5 + 1 + 9) 8 (i.e., 2 + 1) 6 (i.e., 2 + 4) |
Total number of students = 50
Table B can answer a number of questions about the
performance of the students in the test immediately.
For example:
(i) How many students secured below 20 marks in the test?
Answer: 3 students.
(ii) How many students secured 20 or above marks but below 40 marks in the test?
Answer: 15 students.
(iii) How many students secured below 40 marks in the test?
Answer: 3 + 15 = 18 students.
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