Statistics – Exercise 14.3 – (MATHEMATICS) – 9th Class

0

Exercise 14.3

1.  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 figures (in %)

S.No.CausesFemale fatality rate (%)
1.Reproductive health conditions31.8
2.Neuropsychiatric conditions25.4
3.Injuries12.4
4.Cardiovascular conditions4.3
5.Respiratiory conditions4.1
6.Other causes22.0

(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,

Show Answer

Sol. (i) Bar graph representing the causes of female fatility rate (in %):

(ii) Reproductive health conditions is the major cause of illness and death of women.
(iii) Two factors are uneducated and poor background.


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:

SectionNumber of girls per thousand boys
Scheduled Caste (SC)940
Scheduled Tribe (ST)970
Non-SC/ST920
Backward districts950
Non-backward districts920
Rural930
Urban910

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

Show Answer

Sol. (i) Bar graph representing the number of girls (to the nearest ten) per thousand boys in different sections of society.

(ii) The highest percentage of girls per thousand boys and the lowest percentage of boys per thousand boys in different sections of Indian society are from ST and urban sections respectively.


3. 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?

Show Answer

Sol. (i) Bar graph representing seats won by different political parties in the polling outcome of a state assembly elections:

(ii) Party A won the maximum number of seats.


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 – 1263
127 -1355
136 – 1449
145 – 15312
154 – 1625
163 – 1714
172 – 1802

 

(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?

Show Answer

Sol. Lengths are not in continuous intervals, first we make continuous intervals.

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

(i) Histogram representing the length of leaves (in mm).

(ii) Yes, frequency polygon is another graphical representation for the same data.

(iii) No. The given data are in class intervals.


5. The following table gives the lifetimes of 400 neon lamps:

 

Lifetime (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?

Show Answer


Sol. (i) Histogram representing the life times of neon-lamps:

(ii) Number of lamps having life time more than 700
hours is
(74 + 62 + 48), i.e., 184.


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

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.

Show Answer

Sol.

Frequency polygons, representing marks of students of both the sections.


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

Number 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.
[Hint. First make the class intervals continuous.]

Show Answer

Sol. let us represent the data into continuous class-intervals.

Number of ballsClass markRuns of Team ARuns of Team B
0.5 – 6.5 (1-6)3.525
6.5 – 12.5  (7-12)69.51
12.5 – 18.5  (13-18)15.582
18.5 – 24.5   (19-24)21.5910
24.5 – 30.5   (25-30)27.545
30.5 – 36.5   (31-36)33.556
36.5 – 42.5   (37-42)39.563
42.5 – 48.5   (43-48)45.5104
48.5 – 54.5   (49-54)51.568
54.5 – 60.5   (55-60)57.5210

Frequency polygons representing the runs scored by two teams A and B on the first 60 balls are given 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 – 25
2 – 33
3 – 56
5 – 712
7 – 109
 10 – 1510
15 – 174

Draw a histogram to represent the data above.

Show Answer

Sol.

Age (in years)Number o childrenClass sizeLength of the rectangle
1 – 251{5 \over 1} \times 1 = 5
2 – 331{3 \over 1} \times 1 = 3
3 – 562{6 \over 2} \times 1 = 3
5 – 7122{{12} \over 2} \times 1 = 6
7 – 1093{9 \over 3} \times 1 = 3
10 – 15105{{10} \over 5} \times 1 = 2
15 – 1742{4 \over 2} \times 1 = 2


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 lettersNumber of surnames
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.

Show Answer

Sol.

Number of lettersNumber of surnamesClass sizeLength of the rectangle
1 – 463{6 \over 4} \times 2 = 4
4 – 6302{{30} \over 2} \times 2 = 30
6  –  8442{{44} \over 2} \times 2 = 44
8 – 12164{{16} \over 4} \times 2 = 8
12 – 2048{4 \over 8} \times 2 = 1

(i) Histogram representing the number of letters in English alphabet in the surnames is given below.

(i) Maximum number of surnames lies in the interval 6-8.


Leave A Reply

Your email address will not be published.

Click Here to ASK Doubtsx