- In a Mathematics test, the following marks were obtained by 40 students. Arrange
these marks in a table using tally marks.
(a) Find how many students obtained marks equal to or more than 7.
(b) How many students obtained marks below 4?
The fifth mark in a group of five marks should be used as a cross, as shown by ‘||||’. These are tally marks. Thus, |||| || shows the count to be five plus two (i.e. seven) and |||| |||| shows five plus five (i.e. ten).
The table using tally marks is as follows:
- a) There are 5 students who obtained 7, 4 students who obtained 8 and 3 who obtained 9. So, there are 5 + 4 + 3 = 12 students who obtained marks equal to or more than 7.
- b) There are 2 students who obtained 1 mark, 3 obtained 2 marks and 3 obtained 3 marks. So, there are 2 + 3 + 3 = 8 students who obtained marks below 4.
- Following is the choice of sweets of 30 students of Class VI.
Ladoo, Barfi, Ladoo, Jalebi, Ladoo, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo,
Jalebi, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo,
Barfi, Rasgulla, Rasgulla, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo.
(a) Arrange the names of sweets in a table using tally marks.
(b) Which sweet is preferred by most of the students?
- b) Ladoo is preferred by most of the students as the table shows the maximum number for ladoos.
- Catherine threw a dice 40 times and noted the number appearing each time as shown below:
1 3 5 6 6 3 5 4 1 6
2 5 3 4 6 1 5 5 6 1
1 2 2 3 5 2 4 5 5 6
5 1 6 2 3 5 2 4 1 5
Make a table and enter the data using tally marks. Find the number that appeared.
(a) The minimum number of times
(b) The maximum number of times
(c) Find those numbers that appear an equal number of times.
Constructing a table using tally marks we have
- a) From the table, the number 4 has appeared only 4 times, and hence is the number that appeared minimum number of times.
- b) The maximum number of times a number has appeared is 11. Hence 5 appeared the maximum number of times.
- c) 1 and 6 have appeared equal number of times, that is, 7 times.
- Following pictograph shows the number of tractors in five villages.
Observe the pictograph and answer the following questions.
(i) Which village has the minimum number of tractors?
(ii) Which village has the maximum number of tractors?
(iii) How many more tractors village C has as compared to village B.
(iv) What is the total number of tractors in all the five villages?
- a) There are 3 tractor pictures for Village D which is less than the number of tractors for all the other villages. So, Village D has the minimum number of tractors.
- b) There are 8 tractor pictures for Village C which is more than the number of tractors for all the other villages. So, Village C has the maximum number of tractors.
- c) Village B has 5 tractors and village C has 8 tractors. So, there are 8 – 5 = 3 tractors more in village C than in village B.
- d) There are 28 tractor pictures in all, which shows the total number of tractors in all the five villages.
- The number of girl students in each class of a co-educational middle school is depicted by the pictograph:
Observe this pictograph and answer the following questions:
(a) Which class has the minimum number of girl students?
(b) Is the number of girls in Class VI less than the number of girls in Class V?
(c) How many girls are there in Class VII?
- a) There are lesser number of pictures in class VIII when compared to all other classes. So, class VIII
has the minimum number of girl students.
- b) We see that there are 4 pictures for class VI. As we see that,
from the pictograph, there are 4 × 4 = 16 girls in class VI. There are 2 pictures representing 8 girls
and a half picture representing 2 girls. So, there are 10 girls in class V.
Class VI has 16 – 10 = 6 girls more than class V.
- c) There are 3 pictures representing 3 × 4 = 12 students in class VII.
- The sale of electric bulbs on different days of a week is shown below:
What can we conclude from the said pictograph?
- a) Each picture of a bulb represents 2 bulbs according to the pictograph. So, 12 bulbs were sold on Monday, 16 bulbs were sold on Tuesday, 8 bulbs on Wednesday, 10 bulbs on Thursday, 14 bulbs on Friday, 8 bulbs on Saturday and 18 bulbs on Sunday.
- b) Maximum number of bulbs were sold on Sunday.
- c) Same number of bulbs were sold on Wednesday and Saturday and it is the minimum number of bulbs.
- d) Total bulbs sold in a week is 12 + 16 + 8 + 10 + 14 + 8 + 18 = 86 bulbs.
- In a village six fruit merchants sold the following number of fruit baskets in a particular season
Observe this pictograph and answer the following questions:
(a) Which merchant sold the maximum number of baskets?
(b) How many fruit baskets were sold by Anwar?
(c) The merchants who have sold 600 or more number of baskets are planning to buy a godown for the next season. Can you name them?
- a) Each basket in the pictograph represents 100 baskets. There are more number of basket pictures for Martin, which shows that he sold the maximum number.
- b) There are 7 basket images for Anwar in the graph. So, he sold 700 baskets.
- c) Anwar has sold 700 baskets, Martin sold 900 + 50 = 950 baskets and Ranjit Singh sold 800 baskets. So, Anwar, Martin and Ranjit Singh sold more than 600 baskets. Therefore, they are planning to buy a godown.
- Total number of animals in five villages are as follows:
Village A : 80
Village B : 120
Village C : 90
Village D : 40
Village E : 60
Prepare a pictograph of these animals using one symbol to represent 10 animals and answer the following questions:
(a) How many symbols represent animals of village E?
(b) Which village has the maximum number of animals?
(c) Which village has more animals: village A or village C?
The pictograph using the symbol = 10 animals is as follows:
- a) 6 symbols represent animals of village E.
- b) From the pictograph, we see that there is more number of symbols for Village B and hence it has the maximum number of animals.
- c) There are 8 symbols in village A which shows that there are 80 animals in village A and there are 9 symbols in village B, which shows that there are 90 animals in village C. So, village C has more number of animals than village A.
- Total number of students of a school in different years is shown in the following table
- Prepare a pictograph of students using one symbolto represent 100 students and answer the following questions:
(a) How many symbols represent total number of students in the year 2002?
(b) How many symbols represent total number of students for the year 1998?
- Prepare another pictograph of students using any other symbol each representing 50 students. Which pictograph do you find more informative?
The pictograph looks as follows:
- a) 6
- b) 5 complete symbols and 1 incomplete symbol.
- c) The pictograph looks as follows:
This pictograph is more informative.
- The bar graph given below shows the amount of wheat purchased by government during the year 1998-2002. Read the bar graph and write down your observations.
In which year was
(a) the wheat production maximum?
(b) the wheat production minimum?
- a) The maximum wheat production is shown by the longest bar, which is for the year 2002.
- b) The minimum wheat production is shown by the smallest bar and is for the year 1998.
- Observe this bar graph which is showing the sale of shirts in a ready-made shop from Monday to Saturday.
Now answer the following questions:
(a) What information does the above bar graph give?
(b) What is the scale chosen on the horizontal line representing number of shirts?
(c) On which day was the maximum number of shirts sold? How many shirts were sold on that day?
(d) On which day was the minimum number of shirts sold?
(e) How many shirts were sold on Thursday?
- a) The bar graph represents the number of shirts sold from Monday to Saturday.
- b) 1 unit = 5 shirts
- c) The maximum number of shirts sold on a particular day is represented by the longest bar, which is on Saturday. From the graph, we see that 60 shirts were sold on Saturday.
- d) The minimum number of shirts sold on a particular day is represented by the shortest bar, which is on Tuesday.
- e) 35 shirts were sold on Thursday.
- Observe this bar graph which shows the marks obtained by Aziz in half-yearly examination in different subjects. Answer the given questions.
(a) What information does the bar graph give?
(b) Name the subject in which Aziz scored maximum marks.
(c) Name the subject in which he has scored minimum marks.
(d) State the name of the subjects and marks obtained in each of them.
- a) The graph shows the marks obtained by Aziz in various subjects.
- b) Aziz scored maximum marks in Hindi as it is represented by the longest bar in the graph.
- c) He scored minimum marks in Social studies, which is represented by the smallest bar in the graph.
- d) Hindi – 80 marks
English – 60 marks
Mathematics – 70 marks
Science – 50 marks
Social studies – 40 marks
- A survey of 120 school students was done to find which activity they prefer to do in their free time.
Draw a bar graph to illustrate the above data taking scale of 1 unit length = 5 students.
Which activity is preferred by most of the students other than playing?
Taking scale 1 unit length = 5 students, the bar graph looks as below:
Other than playing, the activity that is preferred most is Reading story books.
- The number of Mathematics books sold by a shopkeeper on six consecutive days is shown below:
Draw a bar graph to represent the above information choosing the scale of your choice.
The bar graph with scale 1 unit length = 5 books is as shown below.
- Following table shows the number of bicycles manufactured in a factory during the years 1998 to 2002. Illustrate this data using a bar graph. Choose a scale of your choice.
(a) In which year was the maximum number of bicycles manufactured?
(b) In which year was the minimum number of bicycles manufactured?
The graph below shows the number of bicycles manufactured in a factory during 1998 to 2002.
- a) Maximum number of bicycles was manufactured in the year 2002.
- b) Minimum number of bicycles was manufactured in the year 1999.
- Number of persons in various age groups in a town is given in the following table.
Draw a bar graph to represent the above information and answer the following questions. (take 1 unit length = 20 thousands)
(a) Which two age groups have same population?
(b) All persons in the age group of 60 and above are called senior citizens. How many senior citizens are there in the town?
The bar graph is as shown below:
- a) Age groups 30 – 44 and 45 – 59
- b) All persons in the age group of 60 and above are called senior citizens. There are 80,000 people in the age group 60 – 74 and 40,000 in the age group 75 and above. So totally, there are 80,000 + 40,000 = 1,20,000 senior citizens in the town.