Question-1
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
In the previous question data's are,
(i) Number of students in our class
(ii)Number of fans in our school
(iv)Election results obtained from television and newspaper
(v) Literacy rate figures obtained from educational survey
âˆ´ (i) (ii) and (iii) are primary data, (iv) and (v) are secondary data
Question-3
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
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
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
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
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 â€“ 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
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
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
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
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 womenâ€™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.
(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
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 â€˜Non SC/ ST and â€˜Non-backward Districtsâ€™ sections of the society.
Question-14
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
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
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.
Question-16
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
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 â€“ 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 â€“ Marks |
Frequency |
0 - 10 |
5 |
5 |
10 - 20 | 15 | 19 |
20 - 30 | 25 | 15 |
30 - 40 | 35 | 10 |
40 - 50 | 45 | 1 |
Question-18
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
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
Solution:
Modified Table
[Minimum class â€“ size = 2]
Number of letters |
Number of surnames |
Width of the class |
Length of the rectangle |
1 â€“ 4 | 6 | 3 | = 4 |
4 â€“ 6 | 30 | 2 | = 30 |
6 â€“ 8 | 44 | 2 | = 44 |
8 â€“ 12 | 16 | 4 | = 8 |
12 â€“ 20 |
4 |
8 |
= 1 |
(ii) The class interval in which the maximum number of surnames lie is 6 - 8.
Question-21
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.
âˆ´ 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)
âˆ´ Mode = 3.
Question-22
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. âˆ´ 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) âˆ´ Mode = 52.
Question-23
Solution:
Number of observations (n) = 10, which is even. âˆ´ Median =
=
=
= = x + 1
According to the question,
x + 1 = 63
â‡’ x = 63 - 1
â‡’ x = 62
Hence the value of x is 62.
Question-24
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)
âˆ´ Mode = 14.
Question-25
Solution:
âˆ´ = = = `5083.33
Hence the mean salary is `5083.33
Question-26
(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.