## NCERT 6TH CLASS MATHEMATICS CHAPTER DATA HANDLING

**INTRODUCTION**

**Date :**

**Raw Data :**

**For example :**

**Observation**:

**Type of Data :**

**For example :**

**Organisation of Data :**

**Tabular form :**

**Frequency distribution :**

**Representation of Data :**

**PICTOGRAPH**

**Answer the following questions.**

**(i)**What is the total number of students ?

**Sol.**· represent 3 students and here we have 17 such

**(ii)**Which age group has the lowest number of students ? How many students are there in group.

**Sol.**65 month old age group has the lowest number of students. Three students are there in group.

**(iii)**Which age group has the highest number of students ?

**Sol.**62 months old age group has the highest number of students. 15 students are there in the group.

**(iv)**How many students are there, who are 62 months and below ?

**Sol.**· represents 3 students and here we have 10 such

**(v)**How many students are 62 months and above ?

**Sol.**· represents 3 students and here we have 12 such

**(vi)**How many students are between the age of 61 months and 64 months ?

**Sol.**· represent 3 students and here we have 9 such · who are between the age of 61 months and 64 months

**BAR GRAPH**

**Properties of Bar Graphs :**

**Construction of a bar graph :**

**STEPS :**

**Reading of bar graphs :**

**(i)**What is the total number of students in all the clubs together ?

**(ii)**Which club has more students and how many ?

**(iii)**Which club have equal number of students ?

**(iv)**How many students are there in hockey club ?

**(v)**What information is given in the bar graph ?

**AVERAGE**

**OBJECTIVE TYPE**

Q.1 If one symbol represents 150 trees, then the number of trees represented by are

(A) 600 (B) 700 (C) 750 (D) 500

**Direction : (Q. 2 to Q. 5)**

Using the given bar graph, choose the correct option in the questions given below :

Q.2 Which colour is the least colour common among the cars in the parking lot ?

(A) black (B) white (C) red (D) grey

Q.3 Which colours had the same number of cars parked ?

(A) Black and Grey (B) White and Black (C) White and Red (D) Grey and White

Q.4 What is the ratio of the number of white cars to red cars ?

(A) 5 : 2 (B) 2 : 5 (C) 3 : 1 (D) 1 : 3

Q.5 The total number of cars in the parking lot was

(A) 20 (B) 35 (C) 50 (D) 40

Q.6 The picture graph shows the capacity of 4 containers.

Which container has a capacity of 1/2 litre ?

(A) Bottle (B) Flask (C) Mug (D) Glass

Q.7 Total numbers of animals in five villages are shown in the following table.

If one symbol Å represents 10 animals, the total number of symbols required to represent animals for village C will be :

(A) 5 (B) 7 (C) 8 (D) 9

Q.8 The following pictograph shows the number of varieties of apples stored in a supermarket. The total number of apples stored in the supermarket is

(A) 150 (B) 100 (C) 50 (D) 16

Q.9 Final marks of 20 students are as follows :

53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56

What is the lowest score ?

(A) 37 (B) 100 (C) 62 (D) 48

Q.10 Find the average of first 5 prime numbers

(A) 5 (B) 6 (C) 7.6 (D) 5.6

Q.11 The average of first five multiples of 2 is

(A) 3 (B) 5 (C) 6 (D) 8

Q.12 The arithmetic mean of the numbers 12, 19, 13 and 16 is

(A) 12 (B) 13 (C) 14 (D) 15

**SUBJECTIVE TYPE**

Q.1 The table below shows the number of students playing four different games :

Present this information as a pictograph.

Q.2 Read the bar graph in the figure and answer the following questions :

(i) What is the information given by the bar graph ?

(ii) What is the number of families having 6 members ?

(iii) How many members per family are there in the maximum number of families ? Also tell the number of such families.

(iv) What are the number of members per family for which the number of families are equal ? Also tell the number of scuh families.

Q.3 Draw the bar graph of the following data.

Q.4 Draw the bar graph of the following data

Q.5 Read the graph and answer.

Fill in the chart and prepare a frequency table.

Q.6 A class took a vote to decide where to go for a trip.

(a) How many students are there in the class ?

(b) Where did the majority of students want to go ?

(c) Which was the second choice ?

(d) How many students voted for water park ?

Q.7 Make a bar graph for the following data.

(a) The table shows the number of books read by the class in the past month.

(b) This is the daily routine of Shankar. Make a bar graph representing the time and activities.

Activity Time (hours)

School 6

Sleeping 9

Playing + hobby 3

TV watching 2

Eating + Drinking 1

Other activities 3

(c) This is the result of a traffic survey conducted by Anil in front of his village house for 1 hour.

(d) For the 'Marathon Run for Peace' programme a big group of children took part. The age—wise details of participants are given below.

Q.9 The music group of Class Vl of St. George's School performed a musical programme. The students of Class Vll were asked to grade the programme in a scale of 5 where 1 represents excellent performance, 2 good, 3 ordinary performance, 4 not good, 5 very poor show. This is the result of 80 students of Class Vl.

4, 2, 5, 2, 4, 5, 3, 4, 3, 2, 5, 5, 3, 2, 4, 5, 4, 5, 4, 4, 3, 3, 4, 3, 4, 3, 5, 5, 4, 3, 2, 5, 4, 4, 3, 3, 4, 4, 5, 5, 4, 3, 2, 5, 4, 4, 5, 3, 3, 4, 4, 3, 3, 4, 5, 5, 3, 2, 4, 3, 5, 4, 3, 2, 4, 2, 4, 3, 3, 4, 2, 4, 4, 3, 4, 2, 4, 4

Prepare a frequency table using tally marks.

**ANSWER KEY-1**

**OBJECTIVE :**

1. C 2. C 3. A 4. C 5. D 6. C 7. D

8. A 9. A 10. A 11. C 12. D

**SUBJECTIVE :**

1. (i) maximum number of families with different number of members in family

(ii) 50

(iii) 3, 120

(iv) 8, 9, 10; 10

5. Monday (10), Tuesday (15), Wednesday(10), Thursday (20), Friday(15)

6. (a) 48 (b) Water park

(c) Sea side (d) 16

8. (a) 18000 (b) 14000

(c) 2007

**In questions 1 to 5, out of the four options, only one is correct. write the correct answer.**

1. Using tally marks, which one of the following represents the number eight:

2. The marks (out of 10) obtained by 28 students in a Mathematics test are listed as below:

8, 1, 2, 6, 5, 5, 5, 0, 1, 9, 7, 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9,2, 0

The number of students who obtained marks more than or equal to 5 is

(A) 13 (B) 15 (C) 16 (D) 17

3. In question 2 above, the number of students who scored marks less than 4 is

(A) 15 (B) 13 (C) 12 (D) 10

4. The choices of the fruits of 42 students in a class are as follows:

A , O , B , M , A , G , B , G , A , G , B , M , A , G , M , A , B , G , M , B , A , O , M , O , G , B , O , M G , A , A , B , M , O , M , G , B , A , M , O , M , O,

where A, B, G, M and O stand for the fruits Apple, Banana, Grapes, Mango and Orange respectively.

Which two fruits are liked by an equal number of students?

(A) A and M (B) M and B (C) B and O (D) B and G

5. According to data of question 4, which fruit is liked by most of the students?

(A) O (B) G (C) M (D) A

In questions 6 to 13, state whether the given statements are true (T) or false (F).

6. In a bar graph, the width of bars may be unequal.

7. In a bar graph, bars of uniform width are drawn vertically only.

8. In a bar graph, the gap between two consecutive bars may not be the same.

9. In a bar graph, each bar (rectangle) represents only one value of the numerical data.

10. To represent the population of different towns using bar graph, it is convenient to take one unit length to represent one person.

11. Pictographs and bar graphs are pictorial representations of the numerical data.

12. An observation occurring five times in a data is recorded as | | | | |, using tally marks.

13. In a pictograph, if a symbol represents 50 books in a library shelf, then the symbol represents 25 books.

**In questions 14 to 20, fill in the blanks to make the statements true:**

14. A _______ is a collection of numbers gathered to give some meaningful information.

15. The data can be arranged in a tabular form using _______ marks.

16. A _______ represents data through pictures of objects.

17. In a bar graph, ________ can be drawn horizontally or vertically.

18. In a bar graph, bars of ________ width can be drawn horizontally or vertically with ________ spacing between them.

19. An observation occurring seven times in a data is represented as ________ using tally marks.

20. In a pictograph, if a symbol represents 20 flowers in a basket then stands for ________ flowers.

21. On the scale of 1 unit length = 10 crore, the bar of length 6 units will represent ________ crore and of ——— units will represent 75 crore.

22. In an examination, the grades achieved by 30 students of a class are given below. Arrange these grades in a table using tally marks:

B, C, C, E, A, C, B, B, D, D, D, D, B, C, C, C, A, C, B, E, A, D, C, B, E, C, B, E, C, D

23. The number of two wheelers owned individually by each of 50 families are listed below. Make a table using tally marks.

1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 0, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 4, 1, 3, 1, 1, 2, 1, 1, 1, 1,2, 3, 2, 1, 1

Find the number of families having two or more, two wheelers.

24. The lengths in centimetres (to the nearest centimetre) of 30 carrots are given as follows:

15, 22, 21, 20, 22,15, 15, 20, 20,15, 20, 18,20, 22, 21,

20, 21, 18, 21, 18, 20, 18, 21, 18, 22, 20, 15, 21, 18, 20

Arrange the data given above in a table using tally marks and answer the following questions.

(a) What is the number of carrots which have length more than 20 cm?

(b) Which length of the carrots occur maximum number of times? Minimum number of times?

25. Thirty students were interviewed to find out what they want to be in future. Their responses are llisted as below:

doctor, engineer, doctor, pilot, officer, doctor, engineer, doctor, pilot, officer, pilot, engineer, officer, pilot, doctor, engineer, pilot, officer, doctor, officer, doctor, pilot, engineer, doctor, pilot, officer, doctor,

pilot, doctor, engineer

Arrange the data in a table using tally marks.

26. Following are the choices of games of 40 students of Class VI:

football, cricket, football, kho-kho, hockey, cricket, hockey, kho-kho, tennis, tennis, cricket, football, football, hockey, kho-kho, football, cricket, tennis, football, hockey, kho-kho, football, cricket, cricket,

football, hockey, kho-kho, tennis, football, hockey, cricket, football, hockey, cricket, football, kho- kho, football, cricket, hockey, football.

(a) Arrange the choices of games in a table using tally marks.

(b) Which game is liked by most of the students?

(c) Which game is liked by minimum number of students?

27. Fill in the blanks in the following table which represents shirt size of 40 students of a school.

28. Following pictograph represents some surnames of people listed in the telephone directory of a city

Observe the pictograph and answer the following questions:

(a) How many people have surname ‘Roy’?

(b) Which surname appears the maximum number of times in the telephone directory?

(c) Which surname appears the least number of times in the directory?

(d) Which two surnames appear an equal number of times?

29. Students of Class VI in a school were given a task to count the number of articles made of different materials in the school. The information collected by them is represented as follows:

Observe the pictograph and answer the following questions:

(a) Which material is used in maximum number of articles?

(b) Which material is used in minimum number of articles?

(c) Which material is used in exactly half the number of articles as those made up of metal?

(d) What is the total number of articles counted by the students?

30. The number of scouts in a school is depicted by the following pictograph:

Observe the pictograph and answer the following questions:

(a) Which class has the minimum number of scouts?

(b) Which class has the maximum number of scouts?

(c) How many scouts are there in Class VI?

(d) Which class has exactly four times the scouts as that of Class X?

(e) What is the total number of scouts in the Classes VI to X?

31. A survey was carried out in a certain school to find out the popular school subjects among students of Classes VI to VIII. The data in this regard is displayed as pictograph given below:

(a) Which subject is most popular among the students?

(b) How many students like Mathematics?

(c) Find the number of students who like subjects other than Mathematics and Science.

32. The following pictograph depicts the information about the areas in sqkm (to nearest hundred) of some districts of Chhattisgarh State:

(a) What is the area of Koria district?

(b) Which two districts have the same area?

(c) How many districts have area more than 5000 square kilometres?

33. The number of bottles of cold drinks sold by a shopkeeper on six consecutive days is as follows:

Prepare a pictograph of the data using one symbol to represent 50 bottles.

34. The following table gives information about the circulation of newspapers (dailies) in a town in five languages.

Prepare a pictograph of the above data, using a symbol of your choice, each representing 1000 newspapers.

35. Annual expenditure of a company in the year 2007-2008 is given below:

Prepare a pictograph of the above data using an appropriate symbol to represent Rs 10 lakh.

36. The following bar graph shows the number of houses (out of 100) in a town using different types of fuels for cooking.

(a) Which fuel is used in maximum number of houses?

(b) How many houses are using coal as fuel?

(c) Suppose that the total number of houses in the town is 1 lakh. From the above graph estimate the number of houses using electricity.

37. The following bar graph represents the data for different sizes of shoes worn by the students in a school. Read the graph and answer the following questions.

(a) Find the number of students whose shoe sizes have been collected.

(b) What is the number of students wearing shoe size 6?

(c) What are the different sizes of the shoes worn by the students?

(d) Which shoe size is worn by the maximum number of students?

(e) Which shoe size is worn by minimum number of students?

(f) State whether true or false:

The total number of students wearing shoe sizes 5 and 8 is the same as the number of students wearing shoe size 6.

**ANSWER KEY**

1. D 2. D 3. D 4. D 5. C