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Cumulative Frequency

The marks obt...

Question

The marks obtained by 25 students in a class are as follows

22, 28, 30, 32, 35, 37, 40, 41, 43, 44, 45, 45, 48, 49, 52, 53, 54, 56, 56, 58, 60, 62, 65, 68, 69

(i) Arrange the above data on frequency distribution taking class interval.

20-29, 30-39, 40-49, 50-59, 60-69

(ii) Form the cumulative frequency distribution.

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Solution

(i) The frequency distribution of given data is shown below

(ii) The cumulative frequency distribution of the given data is shown below

$\begin{matrix} Class - Interval & Exclusive Group & Frequency (f)) 20 - 29 & 19.5 - 29.5 & 2 30 - 39 & 29.5 - 39.5 & 4 40 - 49 & 39.5 - 49.5 & 8 50 - 59 & 49.5 - 59.5 & 6 60 - 69 & 59.5 - 69.5 & 5 N = 25 \end{matrix}$

$\begin{matrix} Class - Interval & Cumulative Frequency (cf)) Less than 29.5 & 2 Less than 39.5 & 6 Less than 49.5 & 14 Less than 59.5 & 20 Less than 69.5 & 25 \end{matrix}$

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Q. We are given the following marks secured by 25 students in an examination.
23, 28,30, 32, 35, 36, 36, 40, 41, 43, 44, 44, 45, 48, 49, 52, 53, 54, 56, 56, 58, 61, 62, 65, 68.
(i) Arrange this data in the form of a frequency distribution taking the following class intervals.
20−29, 30−39, 40−49, 50−59 and 60−69
(ii) Draw the frequency polygon and ogive for the above data.

Q. In an examination, 25 students secured the following marks:

23	28	30	32	35	35	36	40	41	43	44	45	45
48	49	52	53	54	56	56	58	61	62	65	68

(i) Arrange these data in the form of a frequency distribution using the following class as intervals:
20−29, 30−39, 40−49, 50−59, and 60−69.
(ii) Arrange the data with cumulative frequencies.

Q. The marks obtained (out of 20) by 30 students of a class in a test are given below:
7, 10, 8, 16, 13, 14, 15, 11, 18, 11, 15, 10, 7, 14, 20, 19, 15, 16, 14, 20, 10, 11, 14, 17, 13, 12, 15, 14, 16, 17.
Prepare a frequency distribution table for the above data using class intervals of equal width in which one class interval in 3–8 (including 2 and excluding 8). From the frequency distribution table so obtained, draw a histogram.

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 the following grouped frequency distribution table class marks are given.

Class Marks	$10$	$22$	$34$	$46$	$58$	$70$
Frequency	$6$	$14$	$20$	$21$	$9$	$5$

(i) Construct class intervals of the data. (Exclusive class intervals)
(ii) Construct less than cumulative frequencies and
(iii) Construct greater than cumulative frequencies

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