Question

The final marks in mathematics of 30 students are as follows:

53, 61, 48, 60, 78, 68, 55, 100, 67, 90
75, 88, 77, 37, 84, 58, 60, 48, 62, 56
44, 58, 52, 64, 98, 59, 70, 39, 50, 60

(i) Arrange these marks in the ascending order. 30 to 39 one group, 40 to 49 second group, etc.
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?

Answer 1

(i)Frequency distribution of the given marks in mathematics of 30 students:

30 − 39	37, 39
40 − 49	44, 48, 48
50 − 59	50, 52, 53, 55, 56, 58, 58, 59
60 − 69	60, 60, 60, 61, 62, 64, 67, 68
70 − 79	70, 75, 77, 78
80 − 89	84, 88
90 − 99	90, 98
100 - 109	100

(ii) From the given data we can see that the highest score is 100.

(iii) The above data shows 37 as the lowest score.

(iv) Range = Highest score − Lowest score = 100 − 37 = 63

(v) If 40 is the pass marks, students who have scored less than 40 have failed. So, the students who have scored 37 and 39 have failed.
∴ Number of students that have failed in the exam = 2

(vi) Students who have scored 75, 77, 78, 84, 88, 90, 98 and 100 are the ones to score more than 75.
∴ Number of students who scored 75 or more = 8

(vii) The observations 51, 54 and 57 have not appeared in the data range of 50-60.

(viii) Students who have scored 37, 39, 44, 48 and 48 are the ones to score less than 50.
∴ Number of students who got less than 50 = 5