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Frequency Polygon Using Histogram

Marks of stud...

Question

Marks of students of a Class are represented in the frequency polygon shown below.
How many students got marks less than 20?

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Solution

There are the four groups who got marks less than 20 in the test.

Respective groups are (0-5), (5-10), (10-15) and (15-20).

Total number of students who got marks less than 20 in the test is the sum of frequency of the respective four groups = 7+10+14+8 = 39.

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Using the data in example (3) above, prepare less than type cumulative frequency table and answer the following questions.

(i) How many students obtained less than 40 marks ?

(ii) How many students obtained less than 10 marks ?

(iii) How many students obtained less than 60 marks ?

(iv) Find the cumulative frequency of the class 50-60.

There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics.

70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47

By taking classes 30-40, 40-50, .... prepare the less than type cumulative frequency table

Using the table, answer the following questions :

(i) How many students, have scored marks less than 80 ?

(ii) How many students have scored marks less than 40 ?

(iii) How many students have scored marks less than 60 ?

Q. The marks obtained by 25 students in a science test are given below. (Marks out of 30)

\begin{matrix} 8 & 7 & 12 & 17 & 20 & 11 & 10 & 10 & 16 \\ 21 & 28 & 25 & 13 & 9 & 27 & 18 & 20 & 19 \\ 7 & 29 & 16 & 15 & 20 & 22 & 27 \end{matrix}

Using this data, answer the following questions:

(1) What is the lowest score obtained?
(2) How many students have obtained this lowest score?
(3) How many students have obtained 20 marks?
(4) What is the frequency of the score 27?
(5) How many students have scored more than 20 marks?

The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type.

55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 2 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.

From the prepared table, answer the following questions :

(i) How many students obtained marks 40 or above 40 ?

(ii) How many students obtained marks 90 or above 90 ?

(iii) How many students obtained marks 60 or above 60 ?

(iv) What is the cumulative frequency of equal to or more than type of the class 0-10?

Q. In a mathematis test following marks were obtained by 40 students of class VI. 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

(i) Find how many students obtained marks equal to or more than 7?
(ii) How many students obtaned marks below 4?

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