Question 1
The frequency table of the weights (in kilograms) of the students is given alongside:
Answer the questions with reference to the given table:
45 ? 50  15 
50 ? 55  14 
55 ? 60  9 
60 ? 65  3 
(i) How many classes are there in the given table?
(ii) What is the frequency of the class 50 to 55?
(iii) Which class has the maximum frequency?
(iv) Which is the class with frequency 9?
(v) What is the lower limit of the class 50 to 55?
(vi) What is the upper limit of the class 55 to 60?
(vii) In which class will a student weighing 57 kg be included?
(viii) How many studentæŠ¯ weights are given in the table?
(ix) State the number of students weighing less than 56 kg?
(x) What is the maximum weight of the student which can be included in the given table?
Solution:
(i) 5
(ii) 14
(iii) 45 to 50
(iv) 55 to 60
(v) 50
(vi) 60
(vii) 55 to 60
(viii) Total number of students = 8 + 15 + 14 + 9 + 3 = 49 students
(ix) Number of students weighing less than 56 kg = 8 + 15 + 14 = 37 students
(x) 65 kg
Question 2
The annual attendance of 58 girls in Std. VIII is given below:169, 168, 171, 180, 165, 190, 195,159, 153, 185, 158, 156, 163, 167,
179, 157, 174, 164, 184, 184, 175,179, 174, 183, 197, 172, 188, 172,
161, 173, 166, 166, 162, 170, 178,182, 178, 177, 171, 177, 177, 171,
193, 187, 192, 182, 176, 176, 180,186, 181, 171, 178, 192, 177, 187, 191, 176,
Prepare a frequency table for the data using the class intervals as:
150155, 155160, 160165, 165170, 170175, 175180, 180185, 185190, 190195, 195200
Solution:
Frequency Distribution Table 

Class interval attendance 
Tally Marks 
Frequency 
150155 
 
1 
155160 
 
4 
160165 

5 
165170 

6 
170175 

10 
175180 

14 
180185 

7 
185190 

5 
190195 

5 
195200 
 
1 

Total 
58 
Question 3
Write true or false with reference to the following frequency table:Â
(ii) The frequency of 35 is 15.
(iii) Class 90 100 has the lowest frequency.
(iv) Class 50  60 has a frequency of 18.
(v) Class 6070 has the highest frequency.
(vi) The frequency of 48 is 18.
(vii) The total number of students is 100.
(viii) There are 10 class intervals.
(ix) If the passing marks are 41, the number of students that failed is 33.
Solution:
(i) False
(ii) True
(iii) True
(iv) False
(v) False
(vi) True
(vii) False
(viii) True
(ix) True
Question 5
Â
(i) Find how many men volunteered for each service?
(ii) What percent of the men volunteered to join Navy force?
Solution:
(i) Number of men joining Army force =
Number of men joining Air force =
Number of men joining Navy force
Number of men joining Marine force
(ii) Percent of the men volunteered to join Navy force
Question 6
The piegraph shows the proportion of workers using various mode for traveling to work.
Study the piegraph and answer the questions given below:
How many workers travel to factory
(i) by bus? (ii) by train? (iii) by cycle? (iv) on foot?
Solution:
Totally there are 1000 workers.
(i) No. of workers traveling by bus =
(ii) No. of workers traveling by train =
(iii) No. of workers traveling by cycle =
(iv) No. of workers traveling on foot =
Question 8
Read the following bar graph and answer the following questions:(i) What information is given by the bar graph?
(ii) In which year the export is minimum?
(iii) In which year the import is maximum?
(iv) In which year the difference of the values of export and import is maximum?
Solution:
(i) The bar graph talks about the export and import in 100 crores of rupees from 1982 to 1987.
(ii) The export is minimum during the year 198283.
(iii) The import is maximum during the year 198687.
(iv) The difference of the values of export and import is maximum during the year 198687.
Question 10
Study the following bar graph which shows the allocation of periods to different subjects in the secondary level in India and Russia.a. How many periods are given to mathematics in each country?
b. Which subject has more periods in India?
c. Which subjects have the same number of periods in both the countries?
d. Which subject is not given proper attention in India while in Russia it gets proper attention?
e. Prepare a table showing the number of periods for each subject in each country.
Solution:
a. India 6 periods. Russia 8 periods
b. Science
c. Social Sciences
d. Field training
e. Table is given below.
Subjects 
India 
Russia 
Native Language Foreign Language Mathematics Social Science Science/Technology Physical Education Art/Music/Library Field Training 
7 6 6 5 9 2 5 0 
6 4 8 5 8 5 1 3 
Total 
40 
40 
Question 11
Illustrate the above by a pie diagram
Solution:
Angle forÂ "at home"?
Angle for "Sleep"?
Angle for "at school"?
Angle for "at playfield"?
Draw a circle of convenient radius and draw radius to start with. Mark off the different angles and divide the circle into corresponding sectors.
Question 12
Look at the histogram and answer the following:1. What is the variable being represented by the histogram? Is the discrete or continuous?
2. How many students are over 170cm tall?
3. How many students are there in all?
4. What is the minimum height possible of the shortest student?
5. What is the minimum height possible of the tallest student?
Solution:
1. The variable being represented is the height of the students in a class. It is continuous since it has to be measured and not counted
2. There are 9 + 5 = 14 students over 170cm tall
3. There are thirty students in all
4. The lowest class interval is 150cm ?155cm, so the minimum height possible is 150cm
5. The highest class interval is 175cm ?180cm, so the maximum height possible in that group is 175cm.
Question 13
List given below was made by a researcher to record the number of bacteria in each sample side. Draw a histogram for the data.Solution:
Make a frequency table for the given observation.
Â
Project Z 

Number of bacteria 
Number of slides 

010 

11 
1020 

10 
2030 

8 
3040 

11 
4050 

8 
5060 

10 
Total 58 
Question 14
Read the following histogram and answer the questions given at the end:(i) What information is depicted by the histogram?
(ii) Which group contains the maximum number of girls?
(iii) Which groups contain the same number of girls?
(iv) Heights of how many girls are 145 cm or more?
Solution:
(i) The histogram depicts the heights (in cm) of 17 girls of a class
(ii) The group 140145 has the maximum number of girls
(iii) Number of girls in the following groups are equal:
125130 and 155160
130135 and 150155
135140 and 145150
(iv) Heights of 6 girls are 145 cm or more
Question 15
A school bag has 3 science books, 3 social studies books, 1 maths book, 2 language books. What is the probability of getting a science book? Is it more or less than getting a social studies book?Solution:
There are in all (3 + 3 + 1 + 2 = 9) outcomes of the event.
Getting a science book consists of 3 outcomes
âˆ´Probability of getting a science book is
In the same way
Probability of getting a social studies book
Therefore probability of getting a science book is same as getting a social studies book.