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Question-1

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

Solution:
(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 and newspaper

(v) Literacy rate figures obtained from educational survey

Question-2

Classify the data in the previous question as primary or secondary data.
 
Solution:
In the previous question data's are,
(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 and newspaper
(v) Literacy rate figures obtained from educational survey
 
∴ (i) (ii) and (iii) are primary data, (iv) and (v) are secondary data

Question-3

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?

Solution:

 

Blood Group

Number of Students (frequency)

A

9

B 6
AB 3
O 12
Total 30


From the above table, O is the most common and AB is the rarest blood group among these students.

Question-4

The distance (in km) of 40 engineers from their residence to their place of work were 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?

Solution:
We observe the following main features from this tabular representation:   

     
(i) The distances (in km) from their residence to their work place of the maximum number of engineers are in the second and third interval, i.e., 5 - 10 and 10 - 15.

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

(iii) The frequencies of the following intervals are same:
5 - 10 and 10 - 15 (Each = 11)
20 - 25 and 25 - 30 (Each = 1)

Question-5

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?

Solution:
(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 %).


 

Question-6

The heights of 50 students, measured to the nearest centimeters, 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?

Solution:
(i) 

(ii) 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.

Question-7

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?

Solution:
(i)

 
(ii) The concentration of sulphur dioxide was more than 0.11 parts per million for
2 + 4 + 2 = 8 days.

Question-8

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.

Solution:
 

 



 
 
 
 

 

Question-9

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?

Solution:
(i) 


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

Question-10


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?

Solution:
(i) 

 

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

 

Question-11

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 0.5 starting from the interval 2-2.5.

Solution:

 

Question-12

A survey conducted by an organization 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

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) being the major cause.
Solution:
(i) Graphical represenation:


(ii) Reproductive health conditions is the major cause of women's ill health and death worldwide.

(iii) Lack of proper diet, lack of advised exercises.

Question-13

The following data on the number of girls (to 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.

Solution:
(i)                         
             
(ii) The two conclusions we can arrive at from the graph are as follows:

a) The numbers of girls to the nearest ten per thousand boys is maximum in Scheduled Tribe section of the society and minimum in 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-backward Districts’ sections of the society.

Question-14

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

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?

Solution:
(i)
 

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

Question-15

(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 that maximum number of leaves are 153 mm long ? WHy.

Solution:

(a)  
It can be observed that the length of leaves is represnted in a discontinuous class interval having a difference of 1 in between them
Therefore 1/2= 0.5 has to be added to each upper class limit and also have to subtract 0.5 from the lower class limits so as to make the class intervals continuous.
 
 
Modified continuous Distribution
 

Length(in mm)

Number of leaves

117.5-126.5

126.5-135.5

135.5-144.5

144.5-153.5

153.5-162.5

162.5-171.5

171.5-180.5

3

5

9

12

5

4

2

 

Taking the length of leaves on X-axis and the number of leaves on y-axis, histogram can be drawn as shown above . In the graph. In the graph 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 (12) has their length in between 144.5mm and 153.5 mm . It is not necessary that all have their lengths as 153 mm

Question-16

The following table gives the lifetimes of 400 neon lamps:
 

Life time(in hours)


Number of lamps

300- 400

400-500

500-600

600-700

700-800

800-900

900-1000

14

56

60

86

74

62

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?

Solution:

(i)

(ii) 74 + 62 + 48 = 184 lamps have a life time of more than 700 hours.

Question-17

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.

Solution:
For section A

Modified Tables

Classes

Class – Marks

Frequency

0 - 10

5

3

10 - 20 15 9
20 - 30 25 17
30 - 40 35 12
40 - 50 45 9

For section B

Classes

Class – Marks

Frequency

0 - 10

5

5

10 - 20 15 19
20 - 30 25 15
30 - 40 35 10
40 - 50 45 1

Question-18

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

Represent the data of both the teams on the same graph by frequency polygons.
[Hint: first make the class intervals continous.]

Solution:
Modified Table
 

Question-19

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.

Solution:

 

Question-20

(ii) Write the class interval in which the maximum number of surnames lie.


Solution:
Modified Table

[Minimum class – size = 2]

Number of letters

Number of surnames

Width of the class

Length of the rectangle

1 – 4 6 3 = 4
4 – 6 30 2 = 30
6 – 8 44 2 = 44
8 – 12 16 4 = 8

12 – 20

4

8

= 1

(ii) The class interval in which the maximum number of surnames lie is 6 - 8.

Question-21

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.

Solution:

(i) Mean

Mean =

             = = = 2.8

(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.

∴ Median =

                     =

                     =
                      = = = 3
(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.

Question-22

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.

Solution:

(i) Mean
Mean =

             =

             = = 54.8
(ii) Median
Arranging the given data in descending order, we have
98, 96, 62, 60, 54, 52, 52, 52, 48, 46, 42,41, 40, 40, 39

Number of observations (n) = 15, which is odd. ∴ Median = observation.

= observation

= 8th observation = 52

(iii) Mode
Arranging the data in descending order, we have

98, 96, 62, 60, 54, 52, 52, 52,48, 46, 42,41, 40, 40, 39

Here, 52 occurs most frequently (3 times) ∴ Mode = 52.

 

Question-23

Of median of 29, 32, 48, 50, x,x+2,72,78,84,95(arranged in ascending) is 63.Find x?

Solution:
Number of observations (n) = 10, which is even. ∴ Median =

=

=

= = x + 1

According to the question,

x + 1 = 63

⇒ x = 63 - 1

⇒ x = 62

Hence the value of x is 62.

Question-24

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

Solution:
The given data is

14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18

Arranging the data in ascending order, we have

14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28

Here 14 occurs most frequently (4 times)

∴ Mode = 14.

Question-25

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

Solution:

= = `5083.33
Hence the mean salary is  `5083.33

Question-26

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.

Solution:
(i) mean marks of a test in mathematics.
(ii) average beauty.




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