SEBA Class 9 Mathematics Chapter 14 Statistics

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SEBA Class 9 Mathematics Chapter 14 Statistics Solutions, SEBA Class 9 Maths Textbook Notes in English Medium, SEBA Class 9 Mathematics Chapter 14 Statistics Solutions in English to each chapter is provided in the list so that you can easily browse throughout different chapter Assam Board SEBA Class 9 Mathematics Chapter 14 Statistics Notes and select needs one.

SEBA Class 9 Mathematics Chapter 14 Statistics

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Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. SEBA Class 9 Mathematics Chapter 14 Statistics Question Answer. These solutions are part of SCERT All Subject Solutions. Here we have given SEBA Class 9 Mathematics Chapter 14 Statistics Solutions for All Subject, You can practice these here.

Statistics

Chapter – 14

Exercise 14.1

Q. 1. Give five examples of data that you can collect from your day- to-day life.

Ans: (i) Number of students in our class.

(ii) Number of fans in our school.

(iii) Electricity bills of our house for the last two years.

(iv) Election results obtained from television newspapers.

(v) Literacy rate figures obtained from educational surveys.

Q. 2. Classify the above data as primary or secondary data.

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Ans: (i), (ii) and (iii) are primary data. (iv) and (v) are secondary data.

Exercise 14.2

Q. 1. The blood groups of 30 students of class VIII are re- corded as follows:

A, B, O, O, AB, O, A, B, A, O, B, A, O, Ο

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. and out which is the most common and which is the rarest blood group among these students.

Ans:

Blood Group	Number of students (frequency)
A	9
B	6
AB	3
O	12
Total	30

O is the most common and AB is the rarest blood group among these students.

Q.2. The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

1	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:

We observe the following main features from this tabular representation:

(i) The distance (in km) from their residence to their workplace of the maximum number of female engineers are in the third interval, i.e., 10-15.

(ii) The distances (in km) from their residence to their workplace of the minimum number of female engineers are in the intervals 20-25 and 25-30 cách.

(ii) The frequencies of the intervals 20-25 and 25-30 are the same. (Each = 1)

Q. 3. The relative humidity (in %) of a certain 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: (i)

(ii) This data is about the month of June (Rainy season)

(iii) Range Highest value – Lowest value = 99.2-84.9 = 14.3 (in %)

Q. 4. The heights of 50 students, measured to the nearest centimetre, 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?

Ans: (i)

(i) The heights of maximum number of students are in the group 160-165 and the heights of minimum number of students are in the group 170-175.

Q.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, 0.04, 0.04-0.08 and so on.

(ii) For how many days, was the concentration of sulphur dioside more than 0.11 parts per million?

Ans: (i)

(ii) The concentration of sulphur dioxide was more than 0.11 parts per million for 2+4+28 days.

Q.6. Three coins were tossed 30 times simultaneously. Each time the number of heads occuring 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:

Q.7. 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?

Ans:

(ii) The most frequently occuring digits are 3 and 9. The most least frequently occurring digit is 0.

Q.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	7	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)

(ii) 2 children watched television for 15 or more hours a week.

Q.9. A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were re- corded 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:

Exercise 14.3

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.

Exercise 14.4

Q.1. The following number of goals were scored by a team in a series of 10 matches: 2, 3, 4, 5, 0, 1, 3,4,3 Find the mean, median and mode of these scores.

Ans: (i) Mean

(ii) Median

Arranging the given data in ascending order, we have

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

Number of observations (n)=10, which is even.

(iii) Mode

Arranging the given data in ascending order, we have

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

Here, 3 occurs most frequently (4 times)

∴ Mode = 3

Q.2. In a Mathematics test given to 15 students, the following marks (out of 100) are recorded: 41, 39, 48, 52, 54, 40, 96, 52, 98, 40 42, 52, 60 Find the mean median and mode of the above marks.

Ans: (i) Mean