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**NCERT Class 9 Mathematics Chapter 12 Statistics**

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**Solutions****NCERT Class 9 Mathematics Chapter 12 Statistics****Statistics**

**Statistics****Chapter – 12**

Exercise 12.1 |

**Q.1. A survey conducted by an organisation for the cause of illness and death among the women between the ages 15-44 (in years) worldwise, found the following figures (in %):**

S. No. | Causes | Female fatality rate (%) |

1. | Reproductive health conditions | 31.8 |

2. | Neuropsychiatric conditions | 25.4 |

3. | Injuries | 12.4 |

4. | Cardiovascular conditions | 4.3 |

5. | Respiratory conditions | 4.1 |

6. | Other causes | 22.0 |

**(i) Represent the information given above graphically.**

**(ii) Which condition is the major cause of women’s ill health and death worldwide?**

**(iii) Try to find out, with the help of your teacher, any two fac- tors which play a major role in the cause in (ii) above being the major cause.**

Ans: (i)

(ii) Reproductive health conditions are the major cause of women’s ill health and death worldwide.

(iii) Lack of proper diet, lack of advice exercises.

**Q.2. The following data on the number of girls (to the nearest ten) per thousand boys in different sections of the society is given below:**

Section | Number of girls per thousand boys |

Scheduled caste | 940 |

Scheduled tribe | 970 |

Non SC/ST | 920 |

Backward districts | 950 |

Non-backward districts | 920 |

Rural | 930 |

Urban | 910 |

**(i) Represent the information above by a bar graph**

**(ii) In the classroom what conclusion can be arrived at from the graph.**

Ans: (i)

(ii) The two conclusions we can arrive at from the graph are as follows:

(a) The number of girls to the nearest ten per thou- sand boys is maximum in the Scheduled Tribe section of the society and minimum in the Urban section of the society.

(b) The number of girls to the nearest ten per thousand boys is the same for ‘Non SC/ST’ and ‘Non-back- ward Districts’ sections of the society.

**Q.3. Given below are the seats won by different political par- ties in the polling outcome of a state assembly elections:**

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

Seats won | 75 | 55 | 37 | 29 | 10 | 37 |

**(i) Draw a bar graph to represent the polling results.**

**(ii) Which political party won the maximum number of seats?**

Ans: (i)

(ii) Political party A won the maximum number of seats.

**Q.4. The length of 40 leaves of a plant are measured correct to one millimetre,and the obtained data is represented in the following table:**

Length (in mm) | Number of leaves |

118-126 | 3 |

127-135 | 5 |

136-144 | 9 |

145-153 | 12 |

154-162 | 5 |

163-171 | 4 |

172-180 | 2 |

**(i) Draw a histogram to represent the given data.**

**(ii) Is there any other suitable graphical representation for the same data?**

Ans: (i) Modified continuous Distribution

Length (in mm) | Number of leaves |

117.5-126.5 | 3 |

126.5-135.5 | 5 |

135.5-144.5 | 9 |

144.5-153.5 | 12 |

153.5-162.5 | 5 |

162.5-171.5 | 4 |

171.5-180.5 | 2 |

(ii) Frequency Polygon.

(iii) No because the maximum number of leaves have their lengths lying in the interval 145-153.

**Q.5. The following table gives the life times of 400 neon lamps:**

Length (in mm) | Number of leaves |

300-400 | 14 |

400-500 | 56 |

500-600 | 60 |

600-700 | 86 |

700-800 | 74 |

800-900 | 62 |

900-1000 | 48 |

**(i) Represent the given information with the help of a histo- gram.**

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

Ans: (i)

(ii) 74+62+48=184 lamps have a lifetime of more than 700 hours.

**Q.6. The following table gives the distribution of students of two sections according to the marks obtained by them:**

Section A | Section B | ||

Marks | Frequency | Marka | Frequency |

0-10 | 3 | 0-10 | 5 |

10-20 | 9 | 10-20 | 19 |

20-30 | 17 | 20-30 | 15 |

30-40 | 12 | 30-40 | 10 |

40-50 | 9 | 40-50 | 1 |

**Represent the marks of the students of both the sections on the same graph by frequency polygons.**

Ans: Modified For section A

Classes | Class-Marks | Frequency |

0-10 | 5 | 3 |

10-20 | 15 | 9 |

20-30 | 25 | 17 |

30-40 | 35 | 12 |

49-50 | 45 | 9 |

For section A

Classes | Class-Marks | Frequency |

0-10 | 5 | 3 |

10-20 | 15 | 19 |

20-30 | 25 | 15 |

30-40 | 35 | 10 |

40-50 | 45 | 1 |

**Q.7. The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:**

Number of balls | Team A | Team B |

1-6 | 2 | 5 |

7-12 | 1 | 6 |

13-18 | 8 | 2 |

19-24 | 9 | 10 |

25-30 | 4 | 5 |

31-36 | 5 | 6 |

37-42 | 6 | 3 |

43-48 | 10 | 4 |

49-54 | 6 | 8 |

55-60 | 2 | 10 |

**Represent the data of both the teams on the same graph by fre- quency polygons.**

Ans: Modified Table

Number of balls | Class-Marks | Team A | Team B |

05-6.5 | 3.5 | 2 | 5 |

6.5-12.5 | 8.5 | 1 | 6 |

12.5-18.5 | 15.5 | 8 | 2 |

18.5-24.5 | 21.5 | 9 | 10 |

24.5-30.5 | 27.5 | 4 | 5 |

30.5-36.5 | 33.5 | 5 | 6 |

36.5-42.5 | 39.5 | 6 | 3 |

42.5-48.5 | 45.5 | 10 | 4 |

48.5-54.5 | 51.5 | 6 | 8 |

54.5-60.5 | 57.5 | 2 | 10 |

**Q. 8. Random survey of the number of children of vari- ous age groups playing in a park was found as follows:**

Age (in years) | Number of children |

1-2 | 5 |

2-3 | 3 |

3-5 | 6 |

5-7 | 12 |

7-9 | 9 |

10-15 | 10 |

15-17 | 4 |

Draw a histogram to represent the data above.

Ans: Modified Table

[Minimum class-size = 1]

**Q.9. 100 surnames randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabets in the surnames was found as follows:**

Number of letters | Number of surnames |

1-4 | 6 |

4-6 | 30 |

6-8 | 44 |

8-12 | 16 |

12-20 | 4 |

**(i) Draw a histogram to depict the given information.**

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

Ans: (i) Modified Table

[Minimum class-size = 2]

(ii) The class interval in which the maximum number of sur- names lie is 6-8.