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#### Page No 642:

#### Question 1:

The following table shows the number of students participating in various games in a school.

Game | Cricket | Football | Basketball | Tennis |

Number of students | 27 | 36 | 18 | 12 |

#### Answer:

#### Page No 642:

#### Question 2:

On a certain day, the temperature in a city was recorded as under:

Time | 5 a. m. | 8 a. m. | 11 a. m. | 3 p. m. | 6 p. m. |

Temperature (in °C) | 20 | 24 | 26 | 22 | 18 |

#### Answer:

#### Page No 642:

#### Question 3:

The approximate velocities of some vehicles are given below:

Name of vehicle | Bicycle | Scooter | Car | Bus | Train |

Velocity (in km/hr) | 27 | 45 | 90 | 72 | 63 |

Draw a bar graph to represent the above data.

#### Answer:

Take the name of vehicle along the *x*-axis and the velocity along the *y*-axis.

#### Page No 642:

#### Question 4:

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:

#### Page No 642:

#### Question 5:

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

Year | 2012−13 | 2013−14 | 2014−15 | 2015−16 | 2016−17 |

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

#### Answer:

#### Page No 642:

#### Question 6:

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

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

Number of scooters sold (in thousands) |
16 | 20 | 32 | 36 | 40 | 48 |

#### Answer:

#### Page No 643:

#### Question 7:

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 |

#### Answer:

#### Page No 643:

#### Question 8:

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 |

#### Answer:

#### Page No 643:

#### Question 9:

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

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

Life expectancy (in years) | 84 | 68 | 80 | 64 | 62 | 73 |

#### Answer:

#### Page No 643:

#### Question 10:

Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

Political party | A | B | C | D | E | F |

Seats won | 65 | 52 | 34 | 28 | 10 | 31 |

Draw a bar graph to represent the polling result.

#### Answer:

#### Page No 643:

#### Question 11:

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 |

#### Answer:

#### Page No 644:

#### Question 12:

Look at the bar graph given below.

Read it carefully 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 he poor?

(iv) What is the average of his marks?

#### Answer:

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

(ii) The student scores very good in mathematics, as the height of the corresponding bar is the highest.

(iii) The student scores bad in Hindi, as the height of the corresponding bar is the lowest.

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

#### Page No 658:

#### Question 1:

The daily wages of 50 workers in a factory are given below:

Daily wages (in ₹) | 340−380 | 380−420 | 420−460 | 460−500 | 500−540 | 540−580 |

Number of workers | 16 | 9 | 12 | 2 | 7 | 4 |

#### Answer:

The given frequency distribution is in exclusive form.

We will represent the class intervals [daily wages (in rupees)] along the *x*-axis & the corresponding frequencies [number of workers] along the *y*-axis.

The scale is as follows:

On* **x*-axis: 1 big division = 40 rupees

On *y*-axis: 1 big division = 2 workers

Because the scale on the* x*-axis starts at 340, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 340

and not at the origin.

We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.

Thus, we will obtain the following histogram:

#### Page No 658:

#### Question 2:

The following table shows the average daily earnings of 40 general stores in a market, during a certain week.

Daily earning (in rupees) | 700−750 | 750−800 | 800−850 | 850−900 | 900−950 | 950−1000 |

Number of stores | 6 | 9 | 2 | 7 | 11 | 5 |

#### Answer:

The given frequency distribution is in exclusive form.

We will represent the class intervals [daily earnings (in rupees)] along the *x*-axis & the corresponding frequencies [number of stores] along the *y*-axis.

The scale is as follows:

On* x*-axis: 1 big division = 50 rupees

On *y*-axis: 1 big division = 1 store

Because the scale on the* x-*axis starts at 700, a kink, i.e., a break is indicated near the origin to signify that the graph is drawn with a scale beginning at 700 and not at the origin.

We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.

Thus, we will obtain the following histogram:

#### Page No 659:

#### Question 3:

The heights of 75 students in a school are given below:

Height (in cm) | 130−136 | 136−142 | 142−148 | 148−154 | 154−160 | 160−166 |

Number of students | 9 | 12 | 18 | 23 | 10 | 3 |

#### Answer:

The given frequency distribution is in exclusive form.

We will represent the class intervals [heights (in cm)] along the *x*-axis & the corresponding frequencies [number of students ] along the *y*-axis.

The scale is as follows:

On* x*-axis: 1 big division = 6 cm

On *y*-axis: 1 big division = 2 students

Because the scale on the* x-*axis starts at 130, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 130

and not at the origin.

We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.

Thus, we will obtain the following histogram:

#### Page No 659:

#### Question 4:

The following table gives the lifetimes of 400 neon lamps:

Lifetime (in hr) | 300−400 | 400−500 | 500−600 | 600−700 | 700−800 | 800−900 | 900−1000 |

Number of lamps | 14 | 56 | 60 | 86 | 74 | 62 | 48 |

(ii) How many lamps have a lifetime of more than 700 hours?

#### Answer:

(i)

(ii) Lamps with lifetime more than 700 hours = 74 + 62 + 48 = 184

#### Page No 659:

#### Question 5:

Draw a histogram for the frequency distribution of the following data.

Class interval | 8−13 | 13−18 | 18−23 | 23−28 | 28−33 | 33−38 | 38−43 |

Frequency | 320 | 780 | 160 | 540 | 260 | 100 | 80 |

#### Answer:

The given frequency distribution is in exclusive form.

We will represent the class intervals along the *x*-axis & the corresponding frequencies along the *y*-axis.

The scale is as follows:

On* x*-axis: 1 big division = 5 units

On *y*-axis: 1 big division = 50 units

Because the scale on the* x-*axis starts at 8, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 8

and not at the origin.

We will construct rectangles with the class intervals as bases and the corresponding frequencies as heights.

Thus, we will obtain the following histogram:

#### Page No 659:

#### Question 6:

Construct a histogram for the following frequency distribution.

Class interval | 5−12 | 13−20 | 21−28 | 29−36 | 37−44 | 45−52 |

Frequency | 6 | 15 | 24 | 18 | 4 | 9 |

#### Answer:

The given frequency distribution is in inclusive form.

So, we will convert it into exclusive form, as shown below:

Class Interval | Frequency |

4.5–12.5 | 6 |

12.5–20.5 | 15 |

20.5–28.5 | 24 |

28.5–36.5 | 18 |

36.5–44.5 | 4 |

44.5–52.5 | 9 |

We will mark class intervals along the *x*-axis and frequencies along the *y*-axis.

The scale is as follows:

On* x*-axis: 1 big division = 8 units

On *y*-axis: 1 big division = 2 units

Because the scale on the* x-*axis starts at 4.5, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 4.5

and not at the origin.

We will construct rectangles with class intervals as bases and the corresponding frequencies as heights.

Thus, we will obtain the histogram as shown below:

#### Page No 659:

#### Question 7:

The following table shows the number of illiterate persons in the age group (10−58 years) in. a town:

Age group (in years) | 10−16 | 17−23 | 24−30 | 31−37 | 38−44 | 45−51 | 52−58 |

Number of illiterate persons | 175 | 325 | 100 | 150 | 250 | 400 | 525 |

#### Answer:

The given frequency distribution is inclusive form.

So, we will convert it into exclusive form, as shown below:

Age (in years) | Number of Illiterate Persons |

9.5-16.5 | 175 |

16.5-23.5 | 325 |

23.5-30.5 | 100 |

30.5-37.5 | 150 |

37.5-44.5 | 250 |

44.5-51.5 | 400 |

51.5-58.5 | 525 |

We will mark the age groups (in years) along the *x*-axis & frequencies (number of illiterate persons) along the *y*-axis.

The scale is as follows:

On* x*-axis: 1 big division = 7 years

On *y*-axis: 1 big division = 50 persons

Because the scale on the* x-*axis starts at 9.5, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 9.5

and not at the origin.

We will construct rectangles with class intervals (age) as bases and the corresponding frequencies (number of illiterate persons) as

heights.

Thus, we obtain the histogram, as shown below:

#### Page No 660:

#### Question 8:

Draw a histogram to represent the following data.

Clas interval | 10−14 | 14−20 | 20−32 | 32−52 | 52−80 |

Frequency | 5 | 6 | 9 | 25 | 21 |

#### Answer:

In the given frequency distribution, class sizes are different.

So, we calculate the adjusted frequency for each class.

The minimum class size is 4.

Adjusted frequency of a class =$\frac{\mathrm{Minimum}\mathrm{class}\mathrm{size}}{\mathrm{Class}\mathrm{size}\mathrm{of}\mathrm{the}\mathrm{class}}\times \mathrm{Its}\mathrm{frequency}$

We have the following table:

Class Interval | Frequency | Adjusted Frequency |

10-14 | 5 | $\frac{4}{4}\times 5=5$ |

14-20 | 6 | $\frac{4}{6}\times 6=4$ |

20-32 | 9 | $\frac{4}{12}\times 9=3$ |

32-52 | 25 | $\frac{4}{20}\times 25=5$ |

52-80 | 21 | $\frac{4}{28}\times 21=3$ |

We mark the class intervals along the

*x*-axis and the corresponding adjusted frequencies along the

*y*-axis.

We have chosen the scale as follows:

On the

*x*- axis,

1 big division = 5 units

On the

*y*-axis,

1 big division = 1 unit

We draw rectangles with class intervals as the bases and the corresponding adjusted frequencies as the heights.

Thus, we obtain the following histogram:

#### Page No 660:

#### Question 9:

100 surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters | 1 − 4 | 4 − 6 | 6 − 8 | 8 − 12 | 12 − 20 |

Number of surnames | 6 | 30 | 44 | 16 | 4 |

(ii) Write the class interval in which the maximum number of surnames lie.

#### Answer:

(i) Here the class intervals are of unequal size. So, we calculate the adjusted frequency using the formula,

$\mathrm{Adjusted}\mathrm{freq}=\frac{\mathrm{min}\mathrm{class}\mathrm{size}}{\mathrm{class}\mathrm{size}\mathrm{of}\mathrm{this}\mathrm{class}}\times \mathrm{freq}$

Class sizes are

4 $-$ 1 = 3

6 $-$ 4 = 2

8 $-$ 6 = 2

12 $-$ 8 = 4

20 $-$ 12 = 8

Minimum class size = 2

Number of letters | Frequency | Width of class | Height of rectangle |

1-4 | 6 | 3 | $\frac{2}{3}\times 6=4$ |

4-6 | 30 | 2 | $\frac{2}{3}\times 30=30$ |

6-8 | 44 | 2 | $\frac{2}{2}\times 44=44$ |

8-12 | 16 | 4 | $\frac{2}{4}\times 16=8$ |

12-20 | 4 | 8 | $\frac{2}{8}\times 4=1$ |

(ii) Maximum number of surnames lie in the interval 6-8.

#### Page No 660:

#### Question 10:

Draw a histogram to represent the following information:

Class interval | 5− 10 | 10 − 15 | 15 − 25 | 25 − 45 | 45 − 75 |

Frequency | 6 | 12 | 10 | 8 | 18 |

#### Answer:

Here the class intervals are of unequal size. So, we calculate the adjusted frequency using the formula,

$\mathrm{Adjusted}\mathrm{freq}=\frac{\mathrm{min}\mathrm{class}\mathrm{size}}{\mathrm{class}\mathrm{size}\mathrm{of}\mathrm{this}\mathrm{class}}\times \mathrm{freq}$

Class sizes are

10 $-$ 5 = 5

15 $-$ 10 = 5

25 $-$ 15 = 10

45 $-$ 25 = 20

75 $-$ 45 = 30

Minimum class size = 5

Class interval | Frequency | Width of class | Height of rectangle |

5-10 | 6 | 5 | $\frac{5}{5}\times 6=6$ |

10-15 | 12 | 5 | $\frac{5}{5}\times 12=12$ |

15-25 | 10 | 10 | $\frac{5}{10}\times 10=5$ |

25-45 | 8 | 20 | $\frac{5}{20}\times 8=2$ |

45-75 | 18 | 30 | $\frac{5}{30}\times 18=3$ |

#### Page No 660:

#### Question 11:

Draw a histogram to represent the following information:

Marks | 0 − 10 | 10 − 30 | 30 − 45 | 45 − 50 | 50 − 60 |

Number of students | 8 | 32 | 18 | 10 | 6 |

#### Answer:

Here the class intervals are of unequal size. So, we calculate the adjusted frequency using the formula,

$\mathrm{Adjusted}\mathrm{freq}=\frac{\mathrm{min}\mathrm{class}\mathrm{size}}{\mathrm{class}\mathrm{size}\mathrm{of}\mathrm{this}\mathrm{class}}\times \mathrm{freq}$

Minimum class size = 5

Marks | Frequency | Width of class | Height of rectangle |

0-10 | 8 | 10 | $\frac{5}{10}\times 8=4$ |

10-30 | 32 | 20 | $\frac{5}{20}\times 32=8$ |

30-45 | 18 | 15 | $\frac{5}{15}\times 18=6$ |

45-50 | 10 | 5 | $\frac{5}{5}\times 10=10$ |

50-60 | 6 | 10 | $\frac{5}{10}\times 6=3$ |

#### Page No 660:

#### Question 12:

In a study of diabetic patients in a village, the following observations were noted.

Age in years | 10−20 | 20−30 | 30−40 | 40−50 | 50−60 | 60−70 |

Number of patients | 2 | 5 | 12 | 19 | 9 | 4 |

#### Answer:

We take two imagined classes—one at the beginning (0–10) and other at the end (70–80)—each with frequency zero.

With these two classes, we have the following frequency table:

Age in Years | Class Mark | Frequency (Number of Patients) |

0–10 | 5 | 0 |

10–20 | 15 | 2 |

20–30 | 25 | 5 |

30–40 | 35 | 12 |

40–50 | 45 | 19 |

50–60 | 55 | 9 |

60–70 | 65 | 4 |

70–80 | 75 | 0 |

Now, we plot the following points on a graph paper:

*A*(5, 0),

*B*(15, 2),

*C*(25, 5),

*D*(35, 12)

*, E*(45, 19),

*F*(55, 9),

*G*(65, 4) and

*H*(75, 0)

Join these points with line segments

*AB, BC, CD, DE, EF, FG, GH ,HI*and

*IJ*to obtain the required frequency polygon.

#### Page No 660:

#### Question 13:

Draw a frequency polygon for the following frequency distribution.

Class interval | 1−10 | 11−20 | 21−30 | 31−40 | 41−50 | 51−60 |

Frequency | 8 | 3 | 6 | 12 | 2 | 7 |

#### Answer:

Though the given frequency table is in inclusive form, class marks in case of inclusive and exclusive forms are the same.

We take the imagined classes ($-$9)–0 at the beginning and 61–70 at the end, each with frequency zero.

Thus, we have:

Class Interval | Class Mark | Frequency |

$-$9–0 | –4.5 | 0 |

1–10 | 5.5 | 8 |

11–20 | 15.5 | 3 |

21–30 | 25.5 | 6 |

31–40 | 35.5 | 12 |

41–50 | 45.5 | 2 |

51–60 | 55.5 | 7 |

61–70 | 65.5 | 0 |

Along the

*x*-axis, we mark –4.5, 5.5, 15.5, 25.5, 35.5, 45.5, 55.5 and 65.5.

Along the

*y*-axis, we mark 0, 8, 3, 6, 12, 2, 7 and 0.

We have chosen the scale as follows :

On the

*x*-axis, 1 big division = 10 units.

On the

*y*-axis, 1 big division = 1 unit.

We plot the points

*A*(–4.5,0),

*B*(5.5, 8),

*C*(15.5, 3),

*D*(25.5, 6),

*E*(35.5, 12),

*F*(45.5, 2),

*G*(55.5, 7) and

*H*(65.5, 0).

We draw line segments

*AB, BC, CD, DE, EF, FG, GH*to obtain the required frequency polygon, as shown below.

#### Page No 660:

#### Question 14:

The ages (in years) of 360 patients treated in a hospital on a particular day are given below.

Age in years | 10−20 | 20−30 | 30−40 | 40−50 | 50−60 | 60−70 |

Number of patients | 90 | 40 | 60 | 20 | 120 | 30 |

#### Answer:

We represent the class intervals along the *x*-axis and the corresponding frequencies along the *y*-axis.

We construct rectangles with class intervals as bases and respective frequencies as heights.

We have the scale as follows:

On the* x*-axis:

1 big division = 10 years

On the *y-*axis:

1 big division = 2 patients

Thus, we obtain the histogram, as shown below.

We join the midpoints of the tops of adjacent rectangles by line segments.

Also, we take the imagined classes 0–10 and 70–80, each with frequency 0. The class marks of these classes are 5 and 75, respectively.

So, we plot the points *A*(5, 0) and *B*(75, 0). We join *A* with the midpoint of the top of the first rectangle and *B* with the midpoint of the top of the last rectangle.

Thus, we obtain a complete frequency polygon, as shown below:

#### Page No 661:

#### Question 15:

Draw a histogram and the frequency polygon from the following data.

Class interval | 20−25 | 25−30 | 30−35 | 35−40 | 40−45 | 45−50 |

Frequency | 30 | 24 | 52 | 28 | 46 | 10 |

#### Answer:

We represent the class intervals along the *x*-axis and the corresponding frequencies along the *y*-axis.

We construct rectangles with class intervals as bases and respective frequencies as heights.

We have the scale as follows:

On the *x*-axis, 1 big division = 5 units.

On the *y-*axis, 1 big division = 5 units.

Because the scale on the* x-*axis starts at 15, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 15

and not at the origin.

Thus, we obtain the histogram, as shown below.

We join the midpoints of the tops of adjacent rectangles by line segments.

Also, we take the imagined classes 15–20 and 50–55, each with frequency 0. The class marks of these classes are 17.5 and 52.5, respectively.

So, we plot the points *A*( 17.5, 0) and *B*(52.5, 0). We join *A* with the midpoint of the top of the first rectangle and *B* with the midpoint of the top of the last rectangle.

Thus, we obtain a complete frequency polygon, as shown below:

#### Page No 661:

#### Question 16:

Draw a histogram for the following data.

Class interval | 600−640 | 640−680 | 680−720 | 720−760 | 760−800 | 800−840 |

Frequency | 18 | 45 | 153 | 288 | 171 | 63 |

#### Answer:

We represent the class intervals along the *x*-axis and the corresponding frequencies along the *y*-axis.

We construct rectangles with class intervals as bases and respective frequencies as heights.

We have the scale as follows:

On the *x*-axis:

1 big division = 40 units

On the *y-*axis:

1 big division = 20 units

Thus, we obtain the histogram, as shown below:

We join the midpoints of the tops of adjacent rectangles by line segments.

Also, we take the imagined classes 560–600 and 840–880, each with frequency 0.

The class marks of these classes are 580 and 860, respectively.

Because the scale on the* x-*axis starts at 560, a kink; i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 560

and not at the origin.

So, we plot the points *A*( 580, 0) and *B*(860, 0). We join *A* with the midpoint of the top of the first rectangle and join *B* with the midpoint of the top of the last rectangle.

Thus, we obtain a complete frequency polygon, as shown below:

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