NCERT Solutions of Chapter: Statistics. NCERT Solutions along with worksheets and notes for Class 9.
Exercise 14.1
(1) Give five examples of data that you can collect from your day – to – day life.
Ans-
Five data that we can collect from our day- to – day life are listed below –
(i) Heights of the students of a class.
(ii) Number of books in the library.
(iii) Population of the city.
(iv) Number of girls and boys student in the class.
(v) Number of schools in the state.
(2) Classify the data in Q.1 above as primary or secondary data.
Ans-
Data are tabulated below as primary or secondary data-
SN | Data | Primary Data | Secondary Data |
1. | Heights of the students of a class. | Primary Data | |
2. | Number of books in the library. | Primary Data | |
3. | Population of the city. | Secondary Data | |
4. | Number of girls and boys student in the class. | Primary Data | |
5. | Number of schools in the state. | Secondary Data |
Ans-
Exercise 14.2
(1) The blood group of 30 students of class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?
Ans-
The data are tabulated below as frequency distribution table –
Blood Groups | Number of students
(i.e., the frequency) |
A | 9 |
B | 6 |
O | 12 |
AB | 3 |
Total 30 |
The most common blood group = O ( Highest frequency)
The rarest blood group = AB ( Lowest frequency)
(2) 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?
Ans-
(3) 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?
Ans-
(4) 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 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?
Ans-
(5) 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.
(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?
Ans-
(6) 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.
Ans-
Ans-
(8) 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 interval as 5 – 10.
(ii) How many children watched television for 15 or more hours a week?
Ans-
(9) 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 09.5 starting from the interval 2 – 2.5.
Ans-
Exercise 14.3
(1) A survey conducted by an organization for the cause of illness and death among the women between the age 15 – 44 (in years) 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 which play a major role in the cause in (ii) above being the major cause.
Ans-
(i) The given data are graphically represented below-
(ii) Reproductive health conditions is the major cause of women’s ill health and death worldwide.
(iii) Two factors which play a major role in the cause in (ii) above being the major cause are-
(a) Less medical facilities.
(b) Less knowledge about hygiene and health issues.
(2) 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 |
Scheduled Caste (SC) | 940 |
Scheduled 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) The above information is represented as bar graph below-
(ii) The results of discussions in class are
(a) The number of girls per thousand boys is highest in scheduled tribe (ST) section.
(b) The number of girls per thousand boys is lowest in urban section.
(c) The number of girls per thousand boys is equal in non SC/ST and Non backward section.
(3) 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?
Ans-
(i) A bar graph is constructed below to represent the polling results.
(ii) Political party A won the maximum number of seats.
(4) 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 (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.[Hint: First make the class intervals continuous]
(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-
(ii)Frequency polygon is the other method to graphical representation of the given data.
(iii) No, it is not true because highest frequency 12 belongs to whole group 145 – 153. It shows that 12 leaves have length of 145 mm to 153 mm.
(5) The following table gives the life times 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 |
700 – 900 | 62 |
900 – 1000 | 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?
Ans-
(i) The given information represented with the help of a histogram below –
(ii) Number of lamps which have a life time of more than 700 hours
= Frequency of group 700 – 800 + Frequency of group 800 – 900 + Frequency of group 900 – 1000
= 74 + 62 + 48
= 184
Hence, 184 lamps have a life time of more than 700 hours.
(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 | Mark | 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.
Ans-
Section A | Section B | ||||
Marks | Class Marks | Frequency | Mark | Class Marks | Frequency |
0 – 10 | 5 | 3 | 0 – 10 | 5 | 5 |
10 – 20 | 15 | 9 | 10 – 20 | 15 | 19 |
20 – 30 | 25 | 17 | 20 – 30 | 25 | 15 |
30 – 40 | 35 | 12 | 30 – 40 | 35 | 10 |
40 – 50 | 45 | 9 | 40 – 50 | 45 | 1 |
The frequency polygons of both sections are represented below –
It is clear from the graph that section A performs better than section B.
(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 teams on the same graph by frequency polygons.
[Hint: First make the class intervals continuous.]
Ans-
Making the class interval continuous
Number of balls | Class – Number of balls | Team A | Team B |
0.5 – 6.5 | 3.5 | 2 | 5 |
6.5 – 12.5 | 9.5 | 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 |
The frequency polygon graph of both teams are represented below –
(8) A random survey of the number of children of various 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 – 10 | 9 |
10 – 15 | 10 |
15 – 17 | 4 |
Draw a histogram to represent the data above.
Ans-
(9) 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet 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 lies.
Ans-
(ii) The class interval in which the maximum number of surnames lies is 6 – 8.
Exercise 14.4
(1) The following number of goals were scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.
Ans-
(2)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.
Ans-
(3) 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
Ans-
(4) Find the mode of 14, 25, 14, 2, 18, 17, 18, 14, 23, 22, 14, 18.
Ans-
(5) Find the mean salary of 60 workers of a factory from the following table:
Salary (In Rs) | Number of workers |
3000 | 16 |
4000 | 12 |
5000 | 10 |
6000 | 8 |
7000 | 6 |
8000 | 4 |
9000 | 3 |
10000 | 1 |
Total 60 |
Ans-
(6) 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.
Ans-
Helping Topics