Question

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?

Answer 1

Given:

The data is given for 62 students in a certain class regarding their mathematics marks out of 100.

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.

The frequency distribution table for the given data is as follows:

Class (Marks obtained)	Tally marks	Frequency (No. of students)
0-10	$\left|\right|\left|\right|$	4
10-20	$\left|\right||$	3
20-30	$\cancel{\left|\right|\left|\right|}\left|\right||$	8
30-40	$\cancel{\left|\right|\left|\right|}\left|\right|\left|\right|$	9
40-50	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}\left|\right||$	13
50-60	$\cancel{\left|\right|\left|\right|}|$	6
60-70	$\cancel{\left|\right|\left|\right|}$	5
70-80	$\cancel{\left|\right|\left|\right|}|$	6
80-90	$\cancel{\left|\right|\left|\right|}$	5
90-100	$\left|\right||$	3
		Total N = 62

The cumulative frequency table more than or equal to type for the given data is as follows:
​

Class (Marks obtained)	Frequency (No. of students)	More than or equal to type cumulative frequency
0-10	4	62
10-20	3	58
20-30	8	55
30-40	9	47
40-50	13	38
50-60	6	25
60-70	5	19
70-80	6	14
80-90	5	8
90-100	3	3
	Total N = 62

(i) The number of students who obtained marks 40 or above 40 is 38.

(ii) The number of students who obtained marks 90 or above 90 is 3.

(iii) The number of students who obtained marks 60 or above 60 is 19.

(iv) The cumulative frequency of equal to or more than type of the class 0-10 is 62.