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

Solution:

The given raw data can be arranged in an ascending order. The class intervals are $30-39,40-49, \ldots 100-109$. Then, take the raw data and place it in the appropriate class intervals.

(i) The marks can be arranged in an ascending order as shown below:

30 to $39 \rightarrow 37,39$

40 to $49 \rightarrow 44,48,48$

50 to $59 \rightarrow 50,52,53$

55, 56, 58, 58, 59

60 to $69 \rightarrow 60,60,60,61,62,64,67,68$

70 to $79 \rightarrow 70,75,77,78$

80 to $89 \rightarrow 84,88$

90 to $99 \rightarrow 90,98$

100 to $109 \rightarrow 100$

(ii) The highest score is 100.

(iii) The lowest score is 37.

(iv) The range is 100-37, i.e. 63 .

(v) If 40 is the passing mark, then the number of students who failed is 2 (i.e. 37, 39).

(vi) The number of students scoring 75 and above is 8 (i.e. 75, 77, 78, 84, 88, 90, 98, 100).

(vii) The marks 51, 54, and 57 do not actually appear between 50 and 60.

(viii) The number of students scoring less than 50 is 5 (i.e. 37, 39, 44, 48, 48).