Question

Given below (Fig. 23.11) is the bar graph indicating the marks obtained out of 50 in mathematics paper by 100 students. Read the bar graph and answer the following questions:


(i) It is decided to distribute work books on mathematics to the students obtaining less then 20 marks, giving one workbook to each of such students. If a work book costs Rs. 5, what sum is required to buy the work books?
(ii) Every student belonging to the highest mark group is entitled to get a prize of Rs. 10.
How much amount of money is required for distributing the prize money?
(iii) Every student belonging to the lowest mark-group has to solve 5 problems per day. How many problem, in all, will be solved by the students of this group per day?
(iv) State whether true of false.
(a) 17% students have obtained marks ranging from 40 to 49.
(b) 59 students have obtained marks ranging from 10 to 29.
(v) What is the number of students getting less than 20 marks?
(vi) What is the number of students getting more than 29 marks?
(vii) What is the number of students getting marks between 9 and 40?
(viii) What is the number of students belonging to the highest mark group?
(ix) What is the number of students obtaining more than 19 marks?

Answer 1

Let us prepare a chart of the 100 students using the data from the bar graph.

Marks	Number of Students
0 − 9	27
10 − 19	12
20 − 29	20
30 − 39	24
40 − 49	17

(i) Number of students with less than 20 marks = 27 + 12 = 39
∴ Required sum to buy the workbooks = Rs. 5 × 39 = Rs. 195

(ii) Highest marks group = 40 − 49
Number of students in this marks group = 17
∴ Required money to distribute the prize = Rs. 10 × 17 = Rs. 170

(iii) Lowest marks group = 0 − 9
Number of students in this marks group = 27
∴ Number of problems that will be solved by the students per day = 5 × 27 = 135

(iv) (a) True
Explanation: Number of students in the marks group 40 − 49 = 17
Total number of students = 100
∴ % of students in the marks group 40 − 49 $=\frac{17}{100}\times 100\%=17\%$
(b) False
Number of students in the marks group 10 − 29
= Number of students in the marks group 0 − 9 + Number of students in the marks group 10 − 19
= 12 + 20 = 32

(v) Number of students scoring less than 20 marks
= Number of students in the marks group 0 − 9 + Number of students in the marks group 10 − 19 = 27 + 12 = 39

(vi) Number of students scoring more than 29 marks
= Number of students in the marks group 30 − 39 + Number of students in the marks group 40 − 49 = 24 + 17 = 41

(vii) Number of students scoring between 9 and 40
= Number of students in the marks group 10 − 19
+ Number of students in the marks group 20 − 29
+ Number of students in the marks group 30 − 39
= 12 + 30 + 24 = 56

(viii) The highest marks group is 40 − 49.
Number of students in this marks group = 17

(ix) Number of students scoring more than 19 marks
= Number of students in the marks group 20 − 29
+ Number of students in the marks group 30 − 39
+ Number of students in the marks group 40 − 49
= 20 + 24 + 17 = 61