NCERT Solutions for Class 9 Maths Chapter 12 Statistics

NCERT
SOLUTIONS
CLASS - 9th

aglase .co

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Class : 9th
Subject : Maths
Chapter : 14
Chapter Name : Statistics

Exercise 14.1

Q1 Give ve examples of data that you can collect from your day-to-day life.

Answer. In our day to life, we can collect the following data.
1. Number Of females per 1000 males in various States Of our country.
2. Weights of students of our class .
3. Production of wheat in the last 10 years in our country .
4. Number of plants in our locality .
5. Rainfall in our city in the last 10 years

Page : 239 , Block Name : Exercise 14.1

Q2 Classify the data in Q.1 above as primary or secondary data.

Answer. The information which is collected by the investigator with a de nite objective in his
mind is called as primary data whereas when the information is gathered from a source which
already had the information stored, it is called as secondary data. It can be observed that the
data in 1, 3, and 5 IS secondary data and the data in 2 and 4 is primary data.

Page : 239 , Block Name : Exercise 14.1

Exercise 14.2

Q1 The blood groups 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?

Answer. It can be observed that 9 students have their blood group as A, 6 as B, 3 as Ad, and 12

Page 1 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

as O.
Therefore, the blood group of 30 students of the class can be represented as follows.

It can be observed clearly that the most common blood group and the rarest blood group
among these students is O and AB respectively as 12 (maximum number of
students) have their blood group as O, and 3 (minimum number of students) have their blood
group as AB.

Page : 245 , Block Name : Exercise 14.2

Q2 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 16 2 7
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 rst interval as 0-5 (5 not included). What main features do you observe from this
tabular representation?

Answer. Let us make the classes as 0-5, 5-10, 10-15, 15-20, 20-25, 25-30 and 30-35.
The frequency distribution table will be as follows:

Page 2 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Page : 245 , Block Name : Exercise 14.2

Q3 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?

Answer. (i) A grouped frequency distribution table of class size 2 has to be constructed. The
class intervals will be -84 - 86, 86 - 88, and -99 - 90...
By observing the data given above, the required table can be constructed as follows.

Page 3 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

(ii) It can be observed that the relative humidity is high. Therefore, the data is about a month of
rainy season.
(iii) Range of data = Maximum value — Minimum value = -99.2 + 84.9 = -14.3

Page : 245 , Block Name : Exercise 14.2

Q4 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?

Answer. (i) A grouped frequency distribution table has to be constructed taking class intervals
160 -165, 165 - 170, etc. dy observing the data given above, the required table can be
constructed as follows.

Page 4 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

(ii) It can be concluded that more than 50% of the students are shorter than 165.

Page : 245 , Block Name : Exercise 14.2

Q5 A study was conducted to nd 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?

Answer. Taking class intervals as 0.00, —0.04, 0.04, —0.08, and so on, a grouped frequency
table can be constructed as follows.

Page 5 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

The number of days for which the concentration of SO is more than 0.11 is the number of days
2

for concentration is in between 0.12 - 0.16, 0.16 - 0.20,
0.20 - 0.24 .
Required number of days=2+4+2=8
There,for 8 days, the concentration of SO is more than 0.11 ppm.
2

Page : 245 , Block Name : Exercise 14.2

Q6 Three coins were tossed 30 times simultaneously. Each time the number of heads occurring
was noted down as follows:
0122123130
1311220121
3001123220
Prepare a frequency distribution table for the data given above.

Answer. By the observation the data given above, the required frequency distribution table can
be constructed as follows.

Page 6 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Page : 246 , Block Name : Exercise 14.2

Q7 The value of π upto 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?

Answer. (i) By the observation of the digits after decimal point, the required table can be
constructed as follows.

(ii) it can observed from the table that the least frequency is 2 of digit 0, and the maximum
frequency is 8 of digit 3 and 9 .therefor , the most frequently occurring digits are 3 and 9 and
the least frequency occurring digit is 0.

Page : 246 , Block Name : Exercise 14.2

Page 7 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Q8 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?

Answer. (i) our class interval will be 0 - 5 , 5 - 10 , 10 - 15 ……
The group distribution frequency table can be constructed as follows.

(ii) the number of children who watched TV for 15 or more hours a week is 2 (i.e…,the number
of children in class interval 15-20 )

Page : 246 , Block Name : Exercise 14.2

Q9 A company manufactures car batteries of particular type. The lives of 4 sch batteries were
recorded as fellows.
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.

Answer. A grouped frequency table of class size 0.5 has to be constructed, starting from class
interval 2 - 2.5.
Therefore, the class intervals Will be 2 - 2.5, 2.5 - 3, 3 - 3.5...
By observing the data given above, the required grouped frequency distribution table can be
constructed as follows.

Page 8 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Page : 246 , Block Name : Exercise 14.2

Exercise 14.3

Q1 A survey conducted by an organisation for the cause of illness and death among the women
between the ages 15 - 44 (in years) worldwide, found the following gures (in %):

(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 nd out, With the help Of your teacher, anv two factors which play a major role in
the cause in (ii) above being the major cause.

Answer. (i) By representing causes on x-axis and family fatality rate on y-axis and choosing an
appropriate scale (I unit 5% for y axis), the graph of the information given above can be
constructed as follows.

Page 9 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

All the rectangle bars are Of the same width and have equal spacing between them.
(ii) Reproductive health condition is the major cause of women's ill health and death worldwide
as 31.8% of women are affected it.
(iii) The factors are as follows:
1. Lack of medical facilities
2. Lack of correct knowledge of treatment

Page : 258 , Block Name : Exercise 14.3

Q2 The following data on the number of girls (to the nearest ten) per thousand boys in different
sections of Indian society is given below.

Page 10 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

(i) Represent the information above a bar graph .
(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Answer. (i) By representing section (variable) on x-axis and number of girls per thousand boys
on y-axis, the graph of the information given above can be constructed by choosing an
appropriate scale (1 unit 100 girls for paxis)

Here, all the rectangle bars are of the same length and have equal spacing in between them.
(ii) It can be observed that maximum number Of girls per thousand boys (i.e., 970) is for ST and
minimum number Of girls per thousand boys (i.e., 910) is for urban.
Also, the number of girls per thousand boys is greater in rural areas than that in urban areas,
backward districts than that in non-backward districts, SC and ST than
that in non-SC/ST.

Page : 258 , Block Name : Exercise 14.3

Q3 Given below are the seats won by different political parties in the polling outcome of a state
assembly elections:

(i) draw a bar graph to represent the polling results.
(ii) which political party won the maximum number of seats.

Answer. (i) By taking polling results on X-axis and seats won as y-axis and choosing an
appropriate scale (1 unit -=10 seats for y-axis), the required graph of the above information can
be constructed as follows.

Page 11 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Here, the rectangle bars are of the same length and have equal spacing in between them.
(ii) Political party 'A' won maximum number of seats.

Page : 259 , Block Name : Exercise 14.3

Q4 The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained
data is represented in the following table:

(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?

Answer. (i) It can be observed that the length of leaves is represented in a discontinuous class
interval having a difference of 1 in between them. Therefore, = 0.5 has to be added to each
1

2

upper class limit and also have to subtract 0.5 from the class limits so as to make the class
intervals continuous.

Page 12 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Taking the length of leaves on x-axis and the number of leaves on y-axis, histogram of this
information can be drawn as above.
Here, 1 unit on y-axis represents 2 leaves.
(ii) Other suitable graphical representation of this data is frequency polygon.
(iii) No, as maximum number Of leaves (i.e., 12) has their length in between 144.5 mm and
153.5 mm. It is not necessary that all ha'.oe their lengths as 153 mm.

Page : 259 , Block Name : Exercise 14.3

Q5 The following table gives the life times of 400 neon lamps:

Page 13 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a life-time of more than 700 hours?

Answer. (i) By taking life time (in hours) of neon lamps on x-axis and the number of lamps on
y-axis, the histogram of the given information can be drawn as follows.

Here, 1 unit on y-axis represents 10 lamps.
(ii) [t can be concluded that the number of neon lamps having their lifetime more than 700 is
the sum of the number of neon lamps having their lifetime as 700 — 800,
800 - goo, and 900 - 1000.
Therefore, the number of neon lamps having their lifetime more than 700 hours is 184. (74 + 62
+48 - 184)

Page : 259 , Block Name : Exercise 14.3

Q6 The following table gives the distribution of students of two sections according to the marks
obtained by them:

Page 14 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

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.

Answer. We can nd the class marks Of the given class intervals by using the following formula.

Upper class limit + Lower class limit
Class mark = 2
.

Taking class marks on x-axis and frequency on y-axis and choosing an appropriate scale (1 unit
- 3 for y-axis), the frequency polygon can be drawn as follows.

Page 15 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

It can be observed that the performance Of students Of section 'A' is better than the students of
section 'B' in terms of good marks.

Page : 260 , Block Name : Exercise 14.3

Q7 The runs scored by two teams A and B on the rst 60 balls in a cricket match are given
below:

Represent the data of both the teams on the same graph by frequency polygons.

Answer. It can be observed that the class inter,zals of the given data are not continuous.
There is a gap of I in between them. Therefore, = 0.5 has to be added to the upper class
1

2

limits and 0.5 has to be subtracted from the lower class limits.
Also, class mark of each interval can be found by using the following formula.
Upper class limit + Lower class limit
Class mark = 2
Continuous data with class mark of each class
interval can Be represented as follows.

Page 16 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

By taking class marks on X-axis and runs scored on y-axis, a frequency polygon can be
constructed as follows.

Page : 260 , Block Name : Exercise 14.3

Q8 A random survey of the number of children of various age groups playing in a park was
found as follows:

Page 17 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Draw a histogram to represent the data above.

Answer. Here, it can be observed that the data has class intervals of varying width. The
proportion Of children per 1 year interval can be calculated as follows.

Taking the age of children on x-axis and proportion children per 1 year interval on y-axis, the
histogram can be drawn as follows.

Page 18 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Page : 261 , Block Name : Exercise 14.3

Q9 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:

(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.

Answer. (i) Here, it can be observed that the data has class intervals of varying width. The
proportion of the number of surnames per 2 letters interval can be calculated as follows:

Page 19 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

By taking the number of letters on X-axis and the proportion of the number of surnames per 2
letters interval on y-axis and choosing an appropriate scale (1 unit - 4 students for y axis), the
histogram can be constructed as follows.

(ii) The class interval in which the maximum number of surnames lies is 6 - 8 as ithas 44
surnames in it i.e., the maximum for this data.

Page : 261 , Block Name : Exercise 14.3

Exercise 14.4

Page 20 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Q1 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

Answer. The number of goals scored by the team is
2,3,4,5,0,1,3,3,4,3
Mean of data =
Sum of all observations

Total number of observations

Mean score =
2+3+4+5+0+1+3+3+4+3

10
28
= = 2.8
10

=2.8 goals
Arranging the number of goals in ascending order,
0,1,2,3,3,3,3,4,4,5
The number Of observations is 10, which is an even number. Therefore, median
Score will be the mean of i.e.,5th and + 1 i.e,6th observation while arranged in
10 10

2 2

ascending or descending order
th th

Median score=
5 observation +6 observation

2
3+3
=
2
6
=
2

=3
Mode Of data is the observation With the maximum frequency in data.
Therefore, the mode score of data is 3 as has the maximum frequency as 4 in the
data.

Page : 269 , Block Name : Exercise 14.4

Q2 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.

Answer. The marks of 15 students in mathematics test are 41, 39, 48, 52, 46, 62, 54, 40, 96, 52,
98, 40, 42, 52, 60
Mean of data = Sum of all observation

Total number of observation

41+39+48+52+46+62+54+40+96+52+40+40+42+60

15
822
= = 54.8
15

Arranging the Scores obtained by 15 students in an ascending order,
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, gs As the number Of observations is 15
which is Odd, therefore, the median Of data Will
= 8th observation whether the data is arranged in an ascending or descending order.
15+1

2

Therefore, median score of data =52
Made of data is observation with the maximum frequency in data. Therefore mode of this data
is 52 having the highest frequency in data a 3.

Page : 269 , Block Name : Exercise 14.4

Page 21 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Q3 The following observations have been arranged in ascending order. If the median of the data
is 63, nd the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Answer. It can be observed that the total number of observations in the given data is 10 (even
number) . therefore the median of this data will be the mean of
,5th and + 1 i.e.,6th observation.
10 10

2 2
th th

Therefore, median of data = 5 observation +6 observation

2
x+x+2
63 =
2
2x+2
63 =
2

63 = x + 1

x = 62

Page : 269 , Block Name : Exercise 14.4

Q4 Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Answer. Arranging the data in an ascending order, 14, 14, 14, 14, 17, 18, IS, 18, 22, 23, 25, 28
It can be observed that 14 has the highest frequency, i.e. 4, in the given data.
Therefore, mode of the given data is 14.

Page : 269 , Block Name : Exercise 14.4

Q5 Find the mean salary of 60 workers of a factory from the following table:

Answer. We know that:
∑ f i xi
Mean=
∑ fi

The value of ∑ f x and ∑ f can be calculated as follows:
i i i

Page 22 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

Mean salary= 305000

60

=5083.33
Therefore,mean salary of 60 workers is Rs. 5083.33

Page : 269 , Block Name : Exercise 14.4

Q6 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.

Answer. When any data has a few observations such that these are very far from the other
observations in it, it is better to calculate the median than the mean of the data as median
gives a better estimate of average in this case.
(i) Consider the following example — the following data represents the heights of the members
of a family.
154.9 cm, 162.8 cm, 170.6 cm, 158.8 cm, 163.3 cm, 166.8 cm, 160.2 cm In this case, it can be
observed that the observations in the given data are close to each other.
Therefore, mean will be calculated as an appropriate measure of central tendency.
(ii) The following data represents the marks obtained by 12 students in a test.
Page 23 of 24 Aglasem Schools

Book : Mathematics Ncert Solutions | Chapter-14 Maths

48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60, gg
In this case, it can be observed that there are some observations which are very far from other
observations. Therefore, here, median will be calculated as an appropriate measure of central
tendency.

Page : 269 , Block Name : Exercise 14.4

Page 24 of 24 Aglasem Schools