A mathematics teacher ask students to collect marks of Mathematics in Half Yearly Exams. She instructed all the students to prepare a frequency distribution table using the data collected. Ram collected the following marks (out of 50) obtained in Mathematics by 60 students of class IX.
21, 10, 30, 22, 33, 5, 37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20, 38, 22, 44, 16, 24, 10, 27, 39, 28, 49, 29, 32, 23, 31, 21, 34, 22, 23, 36, 24, 36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 47, 30, 22, 17
(i) How many students scored more than 20 but less than 30 marks? [1 Marks]
(ii) How many students scored less than 20 marks? [1 Marks]
(iii) How many students scored more than 60% marks? [2 Marks]
OR
What is the class size and class marks of the class interval 30-40? [2 Marks]
Detailed Solution :
(i) The marks more than 20 but less than 30 (i.e., 21–29) are:
{21, 22, 25, 26, 27, 28, 29, 24, 22, 24, 27, 28, 29, 23, 21, 22, 23, 24, 22} = 19
So, there are 19 students who scored more than 20 but less than 30 marks.
(ii) Number of students scored less than 20 marks (i.e. 1 to 19) are :
{10, 5, 12, 15, 18, 19, 18, 16, 10, 7, 16, 17} = 12
So, there are 12 students who scored less than 20 marks.
(iii) No. of students who scored more than 60% marks i.e.
60% of 50
=(60×50)/100
= 3000/100
= 30 Marks
60% of 50
=(60×50)/100
= 3000/100
= 30 Marks
{33, 37, 42, 39, 32, 35, 31, 36, 38, 44, 39, 49, 32, 31, 34, 36, 36, 33, 47, 48, 50, 39, 36, 45, 47} = 25
So, the number of students who scored more than 60% marks is 25.
OR
Class size
= UL-LL
= 40-30
= 10
Class Interval : 30-40?
Class Marks (xi)
= (LL+UL )/ 2
= (30+40)/2
= 70/2
= 35
= (LL+UL )/ 2
= (30+40)/2
= 70/2
= 35