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Q1. Two dice were tossed 100 times. The total points of each toss are represented in the histogram below:   Use the histogram to answer each of the following question. a. Which outcome happened the most times? b. How many times did this outcome discussed in part a happen? c. How many rolls had a total of less than 6 points? d. How many rolls had a total of 10 or more points?

Solution

a. The frequency of bar for 7 points is the highest. Hence, 7 points b. The bar for 7 points has the frequency equal to 17. Hence, the outcome of 7 points happened 17 times. c. The number of rolls less than 6 points is found by adding the frequencies for the groups of 2 points, 3 points, 4 points and 5 points. Required number=2+6+13+11 = 32 d. The number of rolls 10 or more than 10 points is found by adding the frequencies for the groups of 10 points, 11points and 12 points. Required number=7+5+2 = 14

Q2. The following table shows the number of visitors to a park for the months January to March. Month January February March No. of Visitors 150 300 250 a) Construct a bar graph representing the given data. b) What is the percentage increase in visitors in March as compared to January? c) What percentage of visitors came in February as compared with total number of visitors over the three months?

Solution

a) If we choose a scale of 1:50 for the frequency then the vertical bar chart will be as shown.     b) Percentage increase in the visitors in March as compared to January is   c) Percentage of visitors who came in February as compared to the total number of visitors is  

Q3. Read the bar graph given below and answer the following questions: I) Find the year in which there was minimum number of admissions. II) Find the number of students in 3^rd year. III) How many students were admitted by 2^nd year in total? IV) Find the year in which there was maximum number of admissions.

Solution

I) 3^rd year II) 700 III) Total number of students admitted in 1^st and 2^nd year = 900 + 1000 = 1900. IV) 4^th

Q4. Marks obtained by a student in an examination are given below. Draw a pie diagram representing this information: Subjects English Hindi Science Mathematics Marks 100 95 82 83

Solution

  Subjects  Marks  Measure of the central angle English  100    Hindi  95    Science  82    Mathematics   83    Total 360 360    

Q5. In the given pie chart, the central angle of the sector for vegetarian is:

• 1)
• 2)
• 3)
• 4)

Solution

Central angle of the sector for vegetarian

Q6. 85 will not lie in which of the following class intervals?  i. 75-85 ii. 85-95

• 1) ii
• 2) i
• 3) None of the above
• 4) i and ii

Solution

In a continuous class interval, the lower limit is included and the upper limit is excluded. 

Q7. The following data give the number of students using different modes of transport: Mode of transport Bicycle Bus Walk Train Car Number of students 800 300 100 100 140   Represent the above data using a pie diagram.

Solution

  Mode of transport Number of students Measure of the central angle Bicycle  800    Bus  300    Walk  100    Train  100    Car  140    Total 1440 360   On the basis of the table, the pie diagram is as shown:  

Q8. A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.

Solution

Here, S = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H),(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)}   Let E be the event "the die shows an odd number and the coin shows a head".     Therefore, E={(1,H),(3,H),(5,H)}  

Q9. The pie chart given below shows the subjects liked by students of class VIII of a school. What percentage of students like Maths?

• 1) 75%
• 2) 50%
• 3) 20%
• 4) 25%

Solution

Q10. Two dice are tossed. The probability that the total score is a prime number is:

Solution

Clearly, n(S) = (6 x 6) = 36. Let E = Event that the sum is a prime number. Then E = {(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5) }

Q11. The following pie-chart shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie-chart and the answer the questions based on it. i) If for a certain quantity of books, the publisher has to pay Rs. 30,600 as printing cost, than what will be amount of royalty to be paid for these books? ii) What is the central angle of the sector corresponding to the expenditure incurred on Royalty?

Solution

i) Let the amount of Royalty to be paid for these books is Rs. r. Then, 20:15 = 30600:r   ii) Central angle corresponding to Royalty = 15% of 360   

Q12.                        The bar graph shows the marks Brett obtained in his end of year exams. i) How many more percentage points did Brett score in his best subject than in his worst subject? ii) Brett's friend, Luke, scored 12 percentage points higher than Brett in Science. What was Luke's marks for Science?

Solution

i) Brett's best subject was English, in which he scored 60%. Brett's worst subject was Geography, in which he scored 25%. Therefore, he scored (60 - 25)% = 35% more in his best subject than in his worst subject. ii) Brett's mark in Science was 42% Therefore, Luke's mark in Science was 42% + 12% = 54%

Q13. The following table shows various modes of transport used by 1500 students of a school. Mode of transport Bicycle Bus Walk Train Car Number of students 800 300 160 100 140   Draw a bar graph to represent the above data.

Solution

 

Q14. The following data represent scores of 50 students in a calculus test. 72 72 93 70 59 78 74 65 73 80 57 67 72 57 83 76 74 56 68 67 74 76 79 72 61 72 73 76 67 49 71 53 67 65 100 83 69 61 72 68 65 51 75 68 75 66 77 61 64 74 Prepare the continuous grouped frequency distribution table.

Solution

Q15. Read the bar graph given below and answer the following questions: I) In which subject is the student poor? II) What is the average of his marks? III) In which subject is he very good? IV) What information does the bar graph give?  

Solution

I) Mathematics II) Average = 66 III) Hindi IV) The bar graph shows the marks obtained by a student in five subjects.

Q16. Use the given pictograph to answer the following questions. (a) How many cookie boxes were sold by Sam? (b) How many cookie boxes were sold by Emma?

Solution

(a) Number of cookie boxes sold by Sam = 7 x 5 = 35 (b) Number of cookie boxes sold by Emma = 3 x 5 = 15.

Q17. A survey was conducted to know the numbers of cars, buses and motorcycles that passes a particular junction. The result is depicted by the given pie chart. There were 150 buses in the survey.       a) What fraction of the vehicles were motorcycles?   b) What percentage of vehicles passing by the junction were cars? c) Calculate the total number of vehicles in the survey. d) How many cars were included in the survey?

Solution

a) Fraction of motorcycles       b) To convert the angle of a sector into a percentage, we use the formula: Percentage     Percentage of cars       c) Let x be the total number of vehicles       The total number of vehicles is 1,800     d) Number of cars  

Q18. The given pictograph shows rainfall (in cm) in different cities named (A, B, C, D, E and F) during the current year. On the basis of this pictograph, answer the following questions. 1. In which city was the rainfall maximum? 2. In which city was the rainfall minimum? 3. The city A recorded how much more rainfall than the city F?

Solution

1. Maximum rainfall occurred in city B. 2. Minimum rainfall occurred in city F. 3. Rainfall in city A = 7 x 25 cm = 175 cm Rainfall in city F = 1 x 25 cm = 25 cm Difference between rainfalls of city A and F = 175 cm - 25 cm = 150 cm. Thus, city A recorded 150 cm more rainfall than city F.

Q19. The monthly income of a family is Rs. 15000. The monthly expenditure of the family on various items is given below. Items Education Rent Food Clothing Savings Expenditure (in Rs.) 2000 3500 6000 2500 1000 Represent the above data using a pie diagram.

Solution

  Items  Expenditure (in Rs.)  Measure of the central angle Education  2000    Rent  3500    Food  6000    Clothing  2500    Savings  1000    Total 15000 360   On the basis of the table, the pie diagram is as shown: