Question 1. In Summer vacations, Puneet motivated 500 people for blood donation and for this social work he received cash award of â‚¹ 10,000. His father advised him to make a budget plan for spending this amount.
He made following plan :
S.No.  Head  Amount (â‚¹) 
1. 2. 3. 4. 5. 6.  Donation to an orphanage Donation to an oldagehome Books for children of EWS families Gift to grand parents For books to a public library For picnic with classmates  1800 2400 1200 1600 2000 1000 
Total  10,000 
(a) Make a piechart for the above data.
(b) Which mathematical concept has been covered in the above problem?
(c) Which values are depicted by Puneet in his budgetplan?
Sol. (a) To make a piechart, we have to determine central angles corresponding to various heads :
S.No.  Head  Amount (â‚¹)  Central angle 
Total  10,000  360Â° 
The required piechart is as given below :
(b) Statistics
(c)(i) gainful use of prize money
(ii) charity
(iii) caring for others
Question 2. 90 schools participated in a plantation programme. Each school planted 100 plants. After one month the number of plants that survived were recorded as :
95  67  2E  32  65  69  33  98  96 
16  42  32  3E  42  40  69  95  92 
16  83  75  S3  85  37  65  63  42 
89  65  73  31  49  64  76  S3  92 
93,  68  52  79  81  59  82  75  82 
86  90  44  62  31  3E  42  39  S3 
87  56  5E  23  35  S3  85  30  68 
69  S3  36  43  45  S3  75  66  S3 
92  75  89  66  91  SS  89  53  42 
93,  69  90  55  66  52  S3  34  36 
(a) Present the data in a frequency table using classes 2029, 3039, ..... 9099.
(b) From the table find the number of schools where 50% or more plants survived?
(c) Which mathematical concept is used in the above problem?
(d) By taking part in plantation programme which value is depicted by the participating schools?
Sol. (a) The required frequency table is given as:
(b) Total number of plants planted by each school = 100
âˆ´ 50% of 100 = 50
â‡’ Number of schools where 50% or more plants survived = 07 + 16 + 09 + 22 + 12 = 66
(c) Statistics
(d) Betterment of environment.
Question 3. 40 students of class IX contributed different amounts to Prime Ministerâ€™s Relief Fund. Vinod and Preeti were assigned to determine the mean amount of the class. Vinod comes out with his answer as â‚¹160 but Preeti found that the value of â‚¹165 was wrongly copied as â‚¹125 by Vinod and she gave the correct answer.
(a) Find the correct mean.
(b) Which concept of mathematics is used in the above problem?
(c) Which values are depicted by Preeti and other students of class IX?
Sol. (a) Total number of students = 40
â‡’ Number of observations = 40
âˆµ Mean calculated by Vinod = 160
âˆµ Total of 40 observations = 40 Ã— 160 = 6400
But the observation 165 is recorded as 125
âˆ´ Actual total of the 40 observations = (6400 â€“ 125) + 165 = 6440
â‡’ Correct mean calculated by Preeti = (6440/40)= 161
Thus, the correct mean is 161.
(b) Statistics
(c)(i) Accuracy
(ii) Patriotism
Question 4. Mrs. Prabha is a mathematics teacher in a school. She motivated 60 students from 2 sections of class IX to appear in proficiencytest in mathematics. The marks obtained by the students are as :
57  31  46  74  6S  42  54  14  61  33  48  37 
26  8  64  93  72  53  59  38  16  88  75  56 
46  66  45  61  54  27  27  44  63  58  43  31 
61  67  36  49  50  76  38  47  55  77  62  53 
40  71  60  58  45  42  34  46  40  59  42  29 
(a) Construct a group frequency distribution of the above data using classes 0 â€“ 9, 10 â€“ 19, etc. ...
(b) Find the number of students who secured more than 49 marks.
(c) Which mathematical concept is used in the above problem?
(d) By encouraging students of class IX in proficiencytest, which skill is depicted by Mrs. Prabha?
Sol. (a)
(b) From the above frequencytable, we find that :
Number of students securing more than 49 marks = 12 + 10 + 6 + 3 + 1 =32
(c) Statistics
(d) Group inspiration.
Question 5. 30 students from senior classes of a school plan to donate blood in a blooddonation camp.
Their blood groups are recorded as follows :
B,  A,  o,  o,  AB,  o,  A,  0 
B,  A,  B,  A,  o,  o,  A,  AB 
o,  A,  A,  o,  o,  AB,  B,  A 
o,  B,  A,  o,  B,  0 

(a) Represent the given data in the form of a frequencydistribution table.
(b) Which is the most common blood group?
(c) Which mathematical concept is used in the above problem?
(d) By donating bloods, which value is depicted by the students of senior classes?
Sol. (a)
(b) The most common blood group is â€˜Oâ€™.
(c) Statistics
(d) Sacrificial act.