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Cumulative Frequency

Given below a...

Question

Given below are the marks of students in a less than cumulative frequency distribution table. Write the frequencies of the respective classes. Also, write the greater than cumulative frequencies. How many students’ marks are given in the table?

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Solution

The total number of students mentioned in the table is nothing but total of frequencies or less than cumulative frequency of the last class or greater than cumulative frequency of the first class interval, i.e. $75$ .

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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.

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?

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. Prepare the grouped frequency distribution table from the cumulative frequency distribution table given below. Draw the frequency polygon.

Mark	Cumulative Frequency
Less than 5 Less than 15 Less than 25 Less than 35 Less than 45 Less than 55 Less than 65 Less than 75	0 3 5 15 44 70 91 106

Q. Given below are the marks of students in a less than cumulative frequency distribution table. Write the frequencies of the respective classes. Also write the Greater than cumulative frequencies. How many students marks are given in the table?

Class Interval (Marks)	$1 - 10$	$11 - 20$	$21 - 30$	$31 - 40$	$41 - 50$
L.C.F. (No of students)	$12$	$27$	$54$	$67$	$75$

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