NCERT Solutions for Class 9 Maths Chapter 14 Statistics

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Written by Team Trustudies
Updated at 2021-02-18


NCERT solutions for class 9 Maths Chapter 14 Statistics Exercise 14.1

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



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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 5 years.
6. Data of monthly household expenses.

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



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

The information which is collected by the investigator with a definite objective in his mind is called 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, 4 and 6 is primary data.

NCERT solutions for class 9 Maths Chapter 14 Statistics 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?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

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

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

Blood GroupNumber of students
O12
A9
B6
AB3


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.

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 first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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:

Distance from residenceDistance values and No. of entries
(Tally Marks)
No. of engineers(frequency)
0 - 53, 2, 3, 3, 2 = 5 entries5
5 - 105, 7, 7, 9, 7, 8, 5, 9, 6, 7, 6 = 11 entries11
10 - 1510, 11, 13, 12, 10, 12, 11, 12, 12, 14, 12 = 11 entries11
15 - 2019, 17, 18, 17, 16, 15, 18, 15, 15 = 9 entries9
20 - 2520 = 1 entry1
25 - 3025 = 1 entry1
30 - 3531, 32 = 2 entries2

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?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.

Relative Humidity (in %)Number of days (frequency)
84 - 861
86 - 881
88 - 902
90 - 922
92 - 947
94 - 966
96 - 987
98 - 1004
Total30


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

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?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

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

Height (in cm)Number of students (frequency)
150 - 15512
155 - 1609
160 - 16514
165 - 17010
170 - 1755
Total50


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

Q5 ) 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?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.

Concentration of S(O2) (in ppm)Number of days (frequency)
0.00 - 0.044
0.04 - 0.089
0.08 - 0.129
0.12 - 0.162
0.16 - 0.204
0.20 - 0.242
Total30


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

Therefore, for 8 days, the concentration of S(O2) is more than 0.11 ppm.

Q6 ) 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.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

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

Number of HeadsNumber of times (frequency)
06
110
29
35
Total30

Q7 ) The value of ? 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?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

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

DigitNumber of times (frequency)
02
15
25
38
44
55
64
74
85
98
Total50

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 .

Therefore, the most frequently occurring digits are 3 and 9 and the least frequency occurring digit is 0.

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?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

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

HoursNo. of children(frequency)
0 - 510
5 - 1013
10 - 155
15 - 202
Total30


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 )

Q9 ) A company manufactures car batteries of particular type. The lives of 4 sch 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.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.

Lives of batteries (in hours)Number of Batteries
2 - 2.52
2.5 - 36
3 - 3.514
3.5 - 411
4 - 4.54
4.5 - 53
Total40

NCERT solutions for class 9 Maths Chapter 14 Statistics 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

Sr. No.CausesFemale fatality rate (in %)
1.Reproductive health Conditions31.8
2.Neuropsychiatric Conditions25.4
3.injuries12.4
4.Cardio - vascular Conditions4.3
5.Respiratory Conditions4.1
6.Other Conditions22.0
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, anv two factors which play a major role in the cause in ii) above being the major cause.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.

image

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.

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.

SectionNumber of girls per thousand boys (frequency)
Scheduled Caste (SC)940
Scheduled Tribe (ST)970
Non SC / ST920
Backward Districts950
Non - backward Districts920
Rural930
Urban910

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



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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 y - axis)

image

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.

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

Political PartyABCDEF
Seats Won755537291037
i) draw a bar graph to represent the polling results.
ii) which political party won the maximum number of seats.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.

image

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.

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:

Length (in mm)Number of Leaves
118 - 1263
127 - 1355
136 - 1449
145 - 15312
154 - 1625
163 - 1714
172 - 1802
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?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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, 12=0.5 has to be added to each upper class limit and also have to subtract 0.5 from the class limits so as to make the class intervals continuous.

Length (in mm)Number of Leaves
117.5 - 126.53
126.5 - 135.55
135.5 - 144.59
144.5 - 153.512
153.5 - 162.55
162.5 - 171.54
171.5 - 180.52


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.

image

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 have their lengths as 153 mm.

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

Length (in hours)Number of Lamps
300 - 40014
400 - 50056
500 - 60060
600 - 70086
700 - 80074
800 - 90062
900 - 100048
i) Represent the given information with the help of a histogram.
ii) How many lamps have a life-time of more than 700 hours?



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.
image

ii) It 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 - 900, and 900 - 1000.

Therefore, the number of neon lamps having their lifetime more than 700 hours is 184. (74 + 62 + 48 = 184)

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

Section A Section B
MarksFrequencyMarksFrequency
0 - 1030 - 105
10 - 20910 - 2019
20 - 301720 - 3015
30 - 401230 - 4010
40 - 50940 - 501
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.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

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

Classmark=UpperClassLimit+LowerClassLimit2

Section A Section B
MarksClass MarksFrequencyMarksClass MarksFrequency
0 - 10530 - 1055
10 - 2015910 - 201519
20 - 30251720 - 302515
30 - 40351230 - 403510
40 - 5045940 - 50451


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.
image

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.

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

No. of ballsTeam ATeam B
1 - 625
7 - 1216
13 - 1882
19 - 24910
25 - 3045
31 - 3656
37 - 4263
43 - 48104
49 - 5468
55 - 60210
Represent the data of both the teams on the same graph by frequency polygons.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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, has to be added to the upper class 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.

Classmark=UpperClassLimit+LowerClassLimit2
Continuous data with class mark of each class interval can Be represented as follows.

No. of ballsClass MarkTeam ATeam B
0.5 - 6.53.525
6.5 - 12.59.516
12.5 - 18.515.582
18.5 - 24.521.5910
24.5 - 30.527.545
30.5 - 36.533.556
36.5 - 42.539.563
42.5 - 48.545.5104
48.5 - 54.551.568
55.5 - 60.557.5210


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

image

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

Age (in years)No. of children (frequency)
1 - 25
2 - 33
3 - 56
5 - 712
7 - 109
10 - 1510
15 - 174

Draw a histogram to represent the data above.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.

Age (in years)No. of children (frequency)Width of classLength of rectangle
1 - 2515×11=5
2 - 3313×11=3
3 - 5626×12=3
5 - 712212×12=6
7 - 10939×13=3
10 - 1510510×15=2
15 - 17424×12=2


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.

image

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:

Number of letterNumber of surnames (frequency)
1 - 46
4 - 630
6 - 844
8 - 1216
12 - 204

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



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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:

Number of letterNumber of surnames (frequency)Width of classLength of rectangle
1 - 4636×23=4
4 - 630230×22=30
6 - 844244×22=44
8 - 1216416×24=8
12 - 20484×28=1


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.

image

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

NCERT solutions for class 9 Maths Chapter 14 Statistics Exercise 14.4

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



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

The number of goals scored by the team is

2, 3, 4, 5, 0, 1, 3, 3, 4, 3

We know that,
Mean of data
= SumofallobservationsTotalnumberofobservations
Thus, Mean score
= 2+3+4+5+0+1+3+3+4+310=2810
= 2.8 goals

Now, Arranging the number of goals in ascending order, we get,

0, 1, 2, 3, 3, 3, 3, 4, 4, 5

Hence, the number of observations is 10, which is an even number.

Therefore, median Score will be the mean of 102 i.e.,5th and 102+1 i.e,6th observation while arranged in ascending or descending order.
i.e., Median score
= 5thobservation+6thobservation2
=3+32
=62
=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.

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.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.

We know that,

Mean of data
= SumofallobservationsTotalnumberofobservations

? Mean score
= 41+39+48+52+46+62+54+40+96+52+40+40+42+6010
=82215
= 54.8 goals

Arranging the Scores obtained by 15 students in an ascending order, we get,

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

As the number Of observations is 15 which is Odd, therefore, the median Of data Will be 15+12=8th observation whether the data is arranged in an ascending or descending order.

Therefore, median score of data = 52

Mode of data is observation with the maximum frequency in data.

Therefore mode of this data is 52 having the highest frequency in data is 3.

Q3 ) 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



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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 102, 5th and 102+1 i.e., 6th observation.

? median of data
= 5thobservation+6thobservation2
? 63=x+x+22
? 63=2x+22
? 63=x+1
? x=62

Hence, the value of x is 62.

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



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

Arranging the data in an ascending order, we get,

14, 14, 14, 14, 17, 18, 18, 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.

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

Salary (in Rs.)No. of Workers
300016
400012
500010
60008
70006
80004
90003
100001
Total60



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


Answer :

We know that,
Mean
= ?fixi?fi

The value of ?fixi and ?fi can be calculated as follows:

Salary (in Rs.) (xi)No. of Workers (fi)(fi)(xi)
3000163000 × 16 = 48000
4000124000 × 12 = 48000
5000105000 × 10 = 50000
600086000 × 8 = 48000
700067000 × 6 = 42000
800048000 × 4 = 32000
900039000 × 3 = 27000
10000110000 × 1 = 10000
Total?fi=60?fixi=305000

Mean salary
= 30500060
=5083.33

Therefore, mean salary of 60 workers is Rs. 5083.33

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.



NCERT Solutions for Class 9 Maths Chapter 14 Statistics


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.
48, 59, 46, 52, 54, 46, 97, 42, 49, 58, 60.

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.



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