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#### Page No 276:

#### Question 1:

The marks of a student in different subjects are given below:

Subject | Hindi | English | Maths | Science | Social science |

Marks | 43 | 56 | 80 | 65 | 50 |

Draw a bar graph from the above information.

#### Answer:

We can draw the bar graph by following the given steps:

Step 1.- On a graph paper, draw a horizontal line OX as* x*-axis and vertical line OY as *y*-axis.

Step 2.- Along OX, write the names of the subjects at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 10 marks

1 small division = 1 mark

Step 4.- Heights of the various bars are:

Hindi = 43 small divisions = 4 big divisions and 3 small divisions

English = 56 small divisions = 5 big divisions and 6 small divisions

Maths = 80 small divisions = 8 big divisions

Science = 65 small divisions = 6 big divisions and 5 small divisions

Social Science = 50 small divisions = 5 big divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

#### Page No 276:

#### Question 2:

The following table shows the favourite sports of 250 students of a school.

Represent the data by a bar graph.

Sports | Cricket | Football | Tennis | Badminton | Swimming |

No. of students | 75 | 35 | 50 | 25 | 65 |

#### Answer:

We can draw the bar graph by following the given steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y*-axis.

Step 2.- Along OX, write the names of the sports at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 10 students

1 small division = 1 student

Step 4.- Heights of the various bars:

Cricket = 75 small divisions = 7 big divisions and 5 small divisions

Football = 35 small divisions = 3 big divisions and 5 small divisions

Tennis = 50 small divisions = 5 big divisions

Badminton = 25 small divisions = 2 big divisions and 5 small divisions

Swimming = 65 small divisions = 6 big divisions and 5 small divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

#### Page No 276:

#### Question 3:

Given below is a table which shows the year wise strength of a school. Represent this data by a bar graph.

Year | 2011-12 | 2012-13 | 2013-14 | 2014-15 | 2015-16 |

No. of students | 800 | 975 | 1100 | 1400 | 1625 |

#### Answer:

We can draw the bar graph by following the given steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y-*axis.

Step 2.- Along OX, write the years at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 100 students

1 small division = 10 student

Step 4.- Heights of the various bars:

2011-2012 = 80 small divisions = 8 big divisions

2012-2013 = 97.5 small divisions = 9 big divisions and 7.5 small divisions

2013-2014 = 110 small divisions = 11 big divisions

2014-2015 = 140 small divisions = 14 big divisions

2015-2016 = 162.5 small divisions = 16 big divisions and 2.5 small divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 276:

#### Question 4:

The following table shows the number of scooters produced by a company during six consecutive years. Draw a bar graph to represent this data.

Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 |

No. of scooters | 11000 | 14000 | 12500 | 17500 | 15000 | 24000 |

#### Answer:

We can draw the bar graph by following the given steps:-

Step 1.- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y*-axis.

Step 2.- Along OX, write the years at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 2000 scooters

1 small division = 200 scooters

Step 4.- Heights of the various bars:

2011 = 55 small divisions = 5 big divisions and 5 small divisions

2012 = 70 small divisions = 7 big divisions

2013 = 62.5 small divisions = 6 big divisions 2.5 small divisions

2014 = 87.5 small divisions = 8 big divisions and 7.5 small divisions

2015 = 75 small divisions = 7 big divisions and 5 small divisions

2016 = 120 small divisions = 12 big divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 5:

The birth rate per thousand in five countries over a period of time is shown below:

Country | China | India | Germany | UK | Sweden |

Birth rate per thousand | 42 | 35 | 14 | 28 | 21 |

Represent the above data by a bar graph.

#### Answer:

We can draw the bar graph by following the given steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y*-axis.

Step 2.- Along OX, write the names of the countries at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 5 unit

2 small division = 1 unit

Step 4.- Heights of the various bars:

China = 84 small divisions = 8 big divisions and 4 small divisions

India = 70 small divisions = 7 big divisions

Germany = 28 small divisions = 2 big divisions and 8 small divisions

U.K. = 56 small divisions = 5 big divisions and 6 small divisions

Sweden = 42 small divisions = 4 big divisions and 2 small divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 6:

The following data shows India's total population (in millions) from 1961 to 2011.

Year | 1961 | 1971 | 1981 | 1991 | 2001 | 2011 |

Population (in millions) | 360 | 420 | 540 | 680 | 1020 | 1200 |

#### Answer:

The graph obtained is as follows:

#### Page No 277:

#### Question 7:

The following table shows the interest paid by India (in thousand crore rupees) on external debts during the period 1998-99 to 2002-03. Represent the data by a bar graph.

Year | 1998-99 | 1999-2000 | 2000-01 | 2001-02 | 2002-03 |

Interest (in thousand crore rupees) | 70 | 84 | 98 | 106 | 120 |

#### Answer:

We can draw the bar graph by following the given steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y-*axis.

Step 2.- Along OX, write the years at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 10 thousand crore rupees

1 small division = 1 thousand crore rupees

Step 4.- Heights of the various bars:

1998−99 = 70 small divisions = 7 big divisions

1999−2000 = 84 small divisions = 8 big divisions and 4 small divisions

2000−2001 = 98 small divisions = 9 big divisions and 8 small divisions

2001−2002 = 106 small divisions = 10 big divisions and 6 small divisions

2002−2003 = 120 small divisions = 12 big divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 8:

The air distances of four cities from Delhi (in km) are given below:

City | Kolkata | Mumbai | Chennai | Hyderabad |

Distance from Delhi (in km) | 1340 | 1100 | 1700 | 1220 |

Draw a bar graph to represent the above data.

#### Answer:

We can draw the bar graph by following steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y-*axis.

Step 2.- Along OX, write the names of the cities at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 100 km

1 small division = 10 km

Step 4.- Heights of the various bars:

Kolkata = 134 small divisions = 13 big divisions and 4 small divisions

Mumbai = 110 small divisions = 11 big divisions

Chennai = 170 small divisions = 17 big divisions

Hyderabad = 122 small divisions = 12 big divisions and 2 small divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 9:

The following table shows the life expectancy (average age to which people live) in various countries in a particular year. Represent this data by a bar graph.

Country | Japan | India | Britain | Ethiopia | Cambodia |

Life expectancy (in years) | 76 | 57 | 70 | 43 | 36 |

#### Answer:

We can draw the bar graph by following the given steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x-*axis and vertical line OY as *y*-axis.

Step 2.- Along OX, write the names of the countries at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 10 years

1 small division = 1 year

Step 4.- Heights of the various bars:

Japan = 76 small divisions = 7 big divisions and 6 small divisions

India = 57 small divisions = 5 big divisions and 7 small divisions

Britain = 70 small divisions = 7 big divisions

Ethiopia = 43 small divisions = 4 big divisions and 3 small divisions

Cambodia = 36 small divisions = 3 big divisions and 6 small divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 10:

The following table shows the imports (in thousand crore rupees) made by India over the last five years. Draw a bar graph to represent this data.

Year | 2001-02 | 2002-03 | 2003-04 | 2004-05 | 2005-06 |

Imports (in thousand crore rupees) | 148 | 176 | 204 | 232 | 180 |

#### Answer:

We can draw the bar graph by following steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y*-axis.

Step 2.- Along OX, write the years at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 20 thousand crore rupees

1 small division = 2 thousand crore rupees

Step 4.- Heights of the various bars:

2001−02 = 74 small divisions = 7 big divisions and 4 small divisions

2002−03 = 88 small divisions = 8 big divisions and 8 small divisions

2003−04 = 102 small divisions = 10 big divisions and 2 small divisions

2004−05 = 116 small divisions = 11 big divisions and 6 small divisions

2005−06 = 90 small divisions = 9 big divisions

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 11:

The data given below shows the average rainfall in Udaipur from June to November of a certain year. Draw a bar graph to represent this information.

Month | June | July | Aug. | Sept. | Oct. | Nov |

Average rainfall | 25 cm | 30 cm | 40 cm | 20 cm | 10 cm | 5 cm |

#### Answer:

We can draw the bar graph by following the given steps:

Step 1- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y*-axis.

Step 2- Along OX, write the names of the months at the points taken at a uniform gap.

Step 3- Choose the scale:

1 big division = 5 cm

2 small divisions = 1 cm

Step 4- Heights of the various bars:

June = 50 small divisions = 5 big divisions

July = 60 small divisions = 6 big divisions

August = 80 small divisions = 8 big divisions

September = 40 small divisions = 4 big divisions

October = 20 small divisions = 2 big divisions

November = 10 small divisions = 1 big division

Step 5- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 12:

The following table shows the market position of different brands of soaps. Draw a bar graph to represent this data.

Brand | A | B | C | D | Other |

Percentage of buyers | 45 | 25 | 15 | 10 | 5 |

#### Answer:

We can draw the bar graph by following the given steps:

Step 1.- On a graph paper, draw a horizontal line OX as *x-*axis and vertical line OY as *y*-axis.

Step 2.- Along OX, write the names of the brands at the points that are taken at a uniform gap.

Step 3.- Choose the scale:

1 big division = 5%

2 small divisions = 1%

Step 4.- Heights of the various bars:

A = 90 small divisions = 9 big divisions

B = 50 small divisions = 5 big divisions

C = 30 small divisions = 3 big divisions

D = 20 small divisions = 2 big divisions

Others = 10 small divisions = 1 big division

Step 5.- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 277:

#### Question 13:

Gold prices on 4 consecutive Tuesdays were as under:

Week | First | Second | Third | Fourth |

Rate per 10 gm (in Rs) | 8500 | 8750 | 9050 | 9250 |

Draw a bar graph to show this imformation.

#### Answer:

We can draw the bar graph by following the given steps:

Step 1- On a graph paper, draw a horizontal line OX as *x-*axis and vertical line OY as *y*-axis.

Step 2- Along OX, write the names of the week at the points that are taken at a uniform gap.

Step 3- Choose the scale:

1 big division = Rs 500

1 small division = Rs 50

Step 4- Heights of the various bars:

First week = 170 small divisions = 17 big divisions

Second week = 175 small divisions = 17 big divisions and 5 small divisions

Third week = 181 small divisions = 18 big divisions and 1 small division

Fourth week = 185 small divisions = 18 big divisions and 5 small divisions

Step 5- Draw bars of equal width on the *x-*axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 278:

#### Question 14:

Various modes of transport used by 1850 students of a school are given below:

School bus | Private bus | Bicycle | Rickshaw | By foot |

640 | 360 | 490 | 210 | 150 |

Draw a bar graph to represent the above data.

#### Answer:

We can draw the bar graph by following the given steps:

Step 1- On a graph paper, draw a horizontal line OX as *x*-axis and vertical line OY as *y*-axis.

Step 2- Along OX, write the names of the modes of transport at the points taken at a uniform gap.

Step 3- Choose the scale:

1 big division = 50 students

1 small division = 5 student

Step 4- Heights of the various bars:

School bus = 128 small divisions = 12 big divisions and 8 small divisions

Private bus = 72 small divisions = 7 big divisions and 2 small divisions

Bicycle = 98 small divisions = 9 big divisions and 8 small divisions

Rickshaw = 42 small divisions = 4 big divisions and 2 small divisions

By foot = 30 small divisions = 3 big divisions

Step 5- Draw the bars of equal width* *on* x*-axis. The difference between the two bars should also be the same.

We get the following bar graph:

#### Page No 278:

#### Question 15:

Look at the bar graph given below.

Read it care fully and answer the following questions.

(i) What information does the bar graph give?

(ii) In which subject is the student very good?

(iii) In which subject is the poor?

(iv) What is the average of his marks?

#### Answer:

(i) The bar graph shows the marks obtained by a student in an examination in various subjects.

(ii) The student is very good in mathematics.

(iii) The student is poor in Hindi.

(iv) Marks scored in English = 60

Marks scored in Hindi = 35

Marks scored in mathematics = 75

Marks scored in social science = 50

Marks scored in science = 60

∴ Average marks = $\frac{60+35+75+50+60}{5}=\frac{280}{5}=56$

#### Page No 278:

#### Question 16:

In a survey or 85 families of a colony, the number of members in each family was recorded, and the data has been represented by the following bar graph.

Read the bar graph carefully and answer the questions given below:

(i) What information does the bar graph give?

(ii) How many families have 3 members?

(iii) How many people live alone?

(iv) Which type of family is the most common? How many members are there in each family of this kind?

#### Answer:

(i) The bar graph shows the number of members in each of the 85 families.

(ii) 40 families have three members each.

(iii) Number of people living alone = 85 − (5+40+25+15)

= 85 − 85

= 0

(iv) The most common family is that with three members.

Each such family has three members .

#### Page No 279:

#### Question 17:

Given below is a bar graph showing the heights of five mountain peaks.

Read the bar graph carefully and answer the following questions:

(i) Which is the highest peak and what is its height?

(ii) What is the ratio of the heights of the highest peak and the next highest peak?

(iii) Arrange the heights of the given peaks in descending order.

#### Answer:

(i) Mount Everest is the highest peak and it's height is 8800 m.

(ii) Height of the highest peak, Mount Everest = 8800 m

Height of the second highest peak, Kanchenjunga = 8200 m

Ratio = $\frac{8800}{8200}=\frac{44}{41}=44:41$

(iii) Heights of the peaks are 6000 m, 8000 m, 7500 m, 8200 m and 8800 m.

Heights in descending order:

8200 m, 8000 m, 7500 m, 6000 m

#### Page No 279:

#### Question 18:

In a public library, the librarian made the following observations in a particular week.

Days | Mon. | Tues. | Wed. | Thurs. | Fri. | Sat. |

Newspaper readers | 350 | 400 | 500 | 450 | 550 | 450 |

Magazine readers | 200 | 450 | 300 | 250 | 100 | 50 |

(i) Draw a double bar graph choosing an appropriate scale.

(ii) On which day, the number of readers in the library was maximum?

(iii) What is the mean number of magazine readers per day?

#### Answer:

(i)

(ii) On Tuesday the number os readers in the library were maximum = 400 + 450 =850

(iii) Mean nnumber of magazine readers = $\frac{200+450+300+250+100+50}{6}=\frac{1350}{6}=225$

#### Page No 279:

#### Question 19:

On a particular day in a school, the attendance in each of the classes from VI to X has been recorded as under.

Class | VI | VII | VIII | IX | X |

Total no. of students | 95 | 90 | 82 | 75 | 68 |

Number of students present on that day | 92 | 85 | 78 | 69 | 62 |

Using the bar graph, answer the questions given below.

(i) Which class has the maximum number of students?

(ii) Find the ratio of number of students present to the total number of students in Class VII.

(iii) What per cent of Class IX students were absent?

#### Answer:

(i) Maximaum number of students are in Class VI

(ii) Ratio = $\frac{85}{90}=\frac{17}{18}$

(iii) Percentage of class IX absent =$\frac{6}{75}\times 100=8$%

#### Page No 280:

#### Question 20:

Consider the data, showing the average daily hours of sunshine in two cities Aberdeen and Margate for six months of an year.

Month | January | February | March | April | May | June |

Number of hours of sunshine in Aberdeen | 2 | $3\frac{1}{4}$ | 4 | $4\frac{1}{2}$ | $7\frac{3}{4}$ | 8 |

Number of hours of sunshine in Margate | $1\frac{1}{2}$ | 3 | $3\frac{1}{2}$ | 6 | $5\frac{1}{2}$ | $6\frac{1}{2}$ |

Draw a double bar graph, to depict the above information.

(i) In which month does Aberdeen have maximum sunlight?

(ii) In which month does Margate have minimum sunlight?

#### Answer:

(i) Maximum sunlight in Aberdeen is during June (8 hours)

(ii) Minimum sunlight in Margate is during January (1.5 hours)

#### Page No 280:

#### Question 21:

The table given below shows the population of four towns over two years.

Towns | A | B | C | D |

2016 | 640000 | 830000 | 460000 | 290000 |

2017 | 750000 | 920000 | 630000 | 320000 |

(i) Draw a double bar graph using approprtate scale to depict the information given above.

(ii) In which town was the population growth maximum?

(iii) In which town was the population growth least?

#### Answer:

(i)

(ii) Maximum population growth was in Town A

(iii) Least population growth in Town D

#### Page No 280:

#### Question 22:

Study the double bar graph given below and answer the questions that follow.**Figure**

(i) What has been compared in the given double bar graph?

(ii) What is the ratio of minimum temperatures in the year 2015 to the year 2016 in the month of November?

(iii) Name the months in which the minimum temperature in 2015 was greater than that in 2016?

(iv) Find the average minimum temperature for the year 2016 for the given four months.

(v) In which month is the variation in two temperatures maximum?

#### Answer:

(i) Minimum temperature for the monts of Nov, Dec, Jan and Feb of 2015 and 2016 have been compared.

(ii) Ratio of minimum temperature in 2015 to minimum temperature in 2016 during the month of Nov = $\frac{18}{14}=\frac{9}{7}$

$\Rightarrow \mathrm{Ratio}=9:7$

(iii) In November and February the minimum temperature in 2015 was greater than that of 2016.

(iv) Average minimum temperature for the year 2016 = $\frac{14+13+8+9}{4}=\frac{44}{4}=11$º^{ }C

(v) November variation = 18 − 14 = 4

December variation = 13 − 11 = 2

January variation = 8 − 5 = 3

February variation = 11 − 9 = 2

During November the variation in two temperatures is maximum.

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