Statistics is an important chapter in Class 9 Mathematics that deals with data collection, representation, and analysis. This chapter covers key topics such as mean, median, mode, and their applications, along with frequency distribution, cumulative frequency, and graphical representation of data. The concepts learned here are foundational for understanding more advanced statistics in higher classes and are crucial for school exams.
NCERT Solutions for Class 9 Maths Chapter 12 – Statistics are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear explanations, formulae, and solved examples, helping students grasp the concepts of data handling and solve problems efficiently.
NCERT Solutions for Class 9 Maths Chapter 12 – Statistics
Q.
Give five examples of data that you can collect from your day-to-day life.
Q.
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
|
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?
Q.
Find the mean salary of 60 workers of a factory from the following table:
|
Salary (in Rs)
|
Number of workers
|
|
3000
4000
5000
6000
7000
8000
9000
10000
|
16
12
10
8
6
4
3
1
|
|
Total
|
60
|
Q.
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Q.
In a mathematics test given to 15 students, the following marks (out of 100) are recorded:
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.
Q.
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
7 – 12
13 – 18
19 – 24
25 – 30
31 – 36
37 – 42
43 – 48
49 – 54
55 – 60
|
2
1
8
9
4
5
6
10
6
2
|
5
6
2
10
5
6
3
4
8
10
|
Represent the data of both the teams on the same graph by frequency polygons.
Q.
The following table gives the distribution of students of two sections according to the marks obtained by them:
|
Section A
|
Section B
|
|
Marks
|
Frequency
|
Marks
|
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 two frequency polygons. From the two polygons compare the performance of the two sections.
Q.
The following table gives the life times of 400 neon lamps:
|
Life time (in hours)
|
Number of lamps
|
|
300 – 400
400 – 500
500 – 600
600 – 700
700 – 800
800 – 900
900 – 1000
|
14
56
60
86
74
62
48
|
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a life time of more than 700 hours?
Q.
The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:
|
Length (in mm)
|
Number of leaves
|
|
118 – 126
127 – 135
136 – 144
145 – 153
154 – 162
163 – 171
172 – 180
|
3
5
9
12
5
4
2
|
(i) Draw a histogram to represent the given data. (ii) Is there any other suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum numbers of leaves are 153 mm long? Why?
Q.
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below.
|
Section
|
Number of girls per thousand boys
|
|
Schedule Cast (SC)
Schedule Tribe(ST)
Non SC/ST
Backward districts
Non-backward districts
Rural
Urban
|
940
970
920
950
920
930
910
|
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.
Q.
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
5 3 10 20 25 11 13 7 12 31
19 10 12 17 18 11 32 17 16 2
7 9 7 8 3 5 12 15 18 3
12 14 2 9 6 15 15 7 6 12
Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?
Q.
A survey conducted by an organization for the cause of illness and death among the women between the ages 15 – 44(in years) worldwide, found the following figures (in %):
|
S.No.
|
Causes
|
Female fatality rate (%)
|
|
1.
2.
3.
4.
5.
6.
|
Reproductive health conditions
Neuropsychiatric conditions
Injuries
Cardiovascular conditions
Respiratory conditions
Other causes
|
31.8
25.4
12.4
4.3
4.1
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 factors which play a major role in the cause in (ii) above being the major cause.
Q.
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5
3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7
2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8
3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4
4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 - 2.5.
Q.
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:
1 6 2 3 5 12 5 8 4 8
10 3 4 12 2 8 15 1 17 6
3 2 8 5 9 6 8 7 14 12
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.
(ii) How many children watched television for 15 or more hours a week?
Q.
The value of π up to 50 decimal places is given below:
3.14159265358979323846264338327950288419716939937510
(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
(ii) What are the most and the least frequently occurring digits?
Q.
Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:
0 1 2 2 1 2 3 1 3 0
1 3 1 1 2 2 0 1 2 1
3 0 0 1 1 2 3 2 2 0
Prepare a frequency distribution table for the data given above.
Q.
A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:
0.03 0.08 0.08 0.09 0.04 0.17
0.16 0.05 0.02 0.06 0.18 0.20
0.11 0.08 0.12 0.13 0.22 0.07
0.08 0.01 0.10 0.06 0.09 0.18
0.11 0.07 0.05 0.07 0.01 0.04
(i) Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04, 0.04 - 0.08 and so on.
(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?
Q.
The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:
161 150 154 165 168 161 154 162 150 151
162 164 171 165 158 154 156 172 160 170
153 159 161 170 162 165 166 168 165 164
154 152 153 156 158 162 160 161 173 166
161 159 162 167 168 159 158 153 154 159
(i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc.
(ii) What can you conclude about their heights from the table?
Q.
The relative humidity (in %) of a certain city for a month of 30 days was as follows:
98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2
95.1 89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3
95.2 97.3 96.2 92.1 84.9 90.2 95.7 98.3 97.3
96.1 92.1 89
(i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc.
(ii) Which month or season do you think this data is about?
(iii) What is the range of this data?
Q.
Give one example of a situation in which
(i) the mean is an appropriate measure of central tendency.
(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Q. 1) Give five examples of data that you can collect from your day-to-day life.
Ans:
-
To know monthly expenses of 20 houses in our society.
-
To know the number of members in the families of our classmates.
-
To know the pet animal population in our society.
-
To know the shoe size of 25 classmates in our class.
-
To know the number of children below 5 years in Godwin Society.
Q. 2) The value of π up to 50 decimal places is given below: 3.14159265358979323846264338327950288419716939937510
(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
(ii) What are the most and the least frequently occurring digits?
Ans:
(i) Frequency distribution of the digits from 0 to 9:
| Digit |
Frequency |
| 0 |
2 |
| 1 |
5 |
| 2 |
5 |
| 3 |
8 |
| 4 |
4 |
| 5 |
5 |
| 6 |
4 |
| 7 |
4 |
| 8 |
5 |
| 9 |
8 |
(ii) The most frequently occurring digits are 3 and 9.
The least frequently occurring digit is 0.
Q. 3) Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were as follows:
1, 6, 2, 3, 5, 12, 5, 8, 4, 8, 10, 3, 4, 12, 2, 8, 15, 1, 17, 6, 3, 2, 8, 5, 9, 6, 8, 7, 14, 12.
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.
(ii) How many children watched television for 15 or more hours a week?
Ans:
(i) Grouped frequency distribution table:
| Class Interval |
Frequency |
| 0 – 5 |
10 |
| 5 – 10 |
13 |
| 10 – 15 |
5 |
| 15 – 20 |
2 |
| Total |
30 |
(ii) 2 children watched television for 15 or more hours a week.
Q. 4) A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
2.6, 3.0, 3.7, 3.2, 2.2, 4.1, 3.5, 4.5, 3.5, 2.3, 3.2, 3.4, 3.8, 3.2, 4.6, 3.7, 2.5, 4.4, 3.4, 3.3, 2.9, 3.0, 4.3, 2.8, 3.5, 3.2, 3.9, 3.2, 3.2, 3.1, 3.7, 3.4, 4.6, 3.8, 3.2, 2.6, 3.5, 4.2, 2.9, 3.6.
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 - 2.5.
Ans:
Grouped frequency distribution table:
| Class Interval |
Frequency |
| 2 – 2.5 |
2 |
| 2.5 – 3.0 |
6 |
| 3.0 – 3.5 |
14 |
| 3.5 – 4.0 |
11 |
| 4.0 – 4.5 |
4 |
| 4.5 – 5.0 |
3 |
| Total |
40 |
Q. 5) A survey conducted by an organization for the cause of illness and death among women between the ages of 15 – 44 worldwide, 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 factors that play a major role in the cause of (ii) being the major cause.
Ans:
(i) The graphical representation of the given information is shown (page 3).
(ii) Reproductive health condition is the major cause of women’s ill health and death worldwide.
(iii) Two factors contributing to reproductive health conditions:
-
Improper diet
-
Lack of medical facility
Q. 6) The following data shows the number of girls (to the nearest ten) per thousand boys in different sections of Indian society:
| Section |
Number of Girls per Thousand Boys |
| Schedule Cast (SC) |
940 |
| Schedule Tribe (ST) |
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, discuss what conclusions can be arrived at from the graph.
Ans:
(i) Bar graph representation is shown (page 5).
(ii) From the graph, we see that the number of girls per thousand boys is lower in urban areas.
Q. 7) Given below are the seats won by different political parties in a state assembly election:
| 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) A bar graph representing the polling results is shown (page 7).
(ii) Political Party A won the maximum number of seats (75 seats).
Q. 8) The length of 40 leaves of a plant is measured to the nearest millimeter. The 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?
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
Ans:
(i) Histogram representation is shown (page 7).
(ii) A frequency polygon is another suitable graphical representation.
(iii) No, it is not correct to conclude that the maximum number of leaves are 153 mm long because the upper limit of a class interval is not included.
Q. 9) The following table gives the lifetime of 400 neon lamps:
| Life Time (in hours) |
Number of Lamps |
| 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 histogram.
(ii) How many lamps have a lifetime of more than 700 hours?
Ans:
(i) The histogram for the given information is shown (page 8).
(ii) The number of lamps with a lifetime of more than 700 hours is 184 (74 + 62 + 48).
Q. 10) The runs scored by two teams A and B on the first 60 balls in a cricket match:
| 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 |
(i) Represent the data of both teams on the same graph by frequency polygons.
Ans:
The frequency polygons for both teams are shown
FAQs: Class 9 Maths Chapter 12 – Statistics
Q1. Is Statistics important for Class 9 exams?
Yes, it is an important chapter for exams, particularly for mean, median, mode, and frequency distribution.
Q2. What topics are most important in this chapter?
Mean, median, mode, cumulative frequency, and graphical representation.
Q3. Are numericals asked from this chapter?
Yes, mean, median, mode calculation, and frequency distribution problems are commonly asked.
Q4. How do you calculate the mean of a frequency distribution?
Mean = Σf * x / Σf, where f is the frequency and x is the midpoint of each class interval.
Q5. How do NCERT Solutions help?
They provide step-by-step solutions with clear explanations, making it easier for students to understand statistical concepts and apply them in problems.