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Mathematics [3 marks sum]

Graphical Representation · ICSE STD 10 (ICSE - English Medium). 19 questions.

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[3 marks sum]

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19 questions · timed · auto-graded

Question 13 Marks
Construct a frequency distribution table for each of the following distributions.
Marks (more than) 0 10 20 30 40 50 60 70 80 90 100
Cumulative frequency 100 87 65 55 42 36 31 21 18 7 0
Answer
Marks (more than) Cumulative frequency Frequency
0 - 10 100 13
10 - 20 87 22
20 - 30 65 10
30 - 40 55 13
40 - 50 42 6
50 - 60 36 5
60 - 70 31 10
70 - 80 21 3
80 - 90 18 11
90 - 100 7 7
Total 100
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Question 23 Marks
Construct a frequency distribution table for each of the following distributions
Marks (less than) 0 10 20 30 40 50 60 70 80 90 100
Cumulative frequency 0 7 28 54 71 84 105 147 180 196 200
Answer
Marks (less than) Cumulative frequency Frequency
0-10 7 7
10-20 28 28-7=21
20-30 54 54-28=26
30-40 17 71-54=17
40-50 84 84-71=13
50-60 105 105-84=21
60-70 147 147-105=42
70-80 180 180-147
80-90 196 196-180=16
90-100 200 200-196=4
Total 200
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Question 33 Marks
Use graph paper for this question.
The table given below shows the monthly wages of some factory workers
(i) Using the table, calculate the cumulative frequencies of workers
(ii) Draw a cumulative frequency curve.
Use 2 cm = ₹ 500, starting the origin at ₹ 6500 on x-axis, and 2 cm = 10 workers on the y – axis.
Wages (in Rs) 6500-7000 7000-7500 7500-8000 8000-8500 8500-9000 9000-9500 9500-10000
No of workers 10 18 22 25 17 10 8
Answer
Wages No. of workers c.f.
6500-7000 10 10
7000-7500 18 28
7500-8000 22 50
8000-8500 25 75
8500-9000 17 92
9000-9500 10 102
9500-10000 8 110

Total = 110
Now plot the points (7000,10), (7500,28), (8000,50), (8500,75), (9000,92), (9500,102) and (10000,110) and join them to obtain an ogive.
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Question 43 Marks
Class mark 12.5 17.5 22.5 27.5 32.5 32.5 42.5
Frequency 12 17 22 27 30 21 16
(a) From the distribution, given above, construct a frequency table.
(b) Use the table obtained in part (a) to draw: (i) a histogram, (ii) an ogive
Answer
(a) Difference in consecutive class marks = 17.5 − 12.5 = 5
⇒first class interval will be 10-15 and so on.
Class Mark Class Interval Frequency c.f.
12.5 10-15 12 12
17.5 15-20 17 29
22.5 20-25 22 51
27.5 25-30 27 78
32.5 30-35 30 108
37.5 35-40 21 129
42.5 40-45 16 145

Total = 145

(b) Now plot the points (15,12), (20,29), (25,51), (30,78), (35,108), (40,129), (45,145) and join them to obtain an ogive.
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Question 53 Marks
Use the information given in the adjoining histogram to construct a frequency table.
Use this table to construct an ogive.
Answer
Class Interval Frequency c.f.
8-12 9 9
12-16 16 25
16-20 22 47
20-24 18 65
24-28 12 77
28-32 4 81

(b) Now plot the points (12, 9), (16, 25), (20, 47), (24, 65), (28, 77), (32, 81) and join them to obtain an ogive.
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Question 63 Marks
Construct a frequency distribution table for the numbers given below, using the class intervals
21 – 30, 31 – 40 ………… etc.
75, 65, 57, 26, 33,44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36 and 47.
Use the table obtained to draw: (1) a histrogram (2) an ogive
Answer
Class Interval Tally Frequency c.f.
20-30 || || 4 4
31-40 ∦∦ ∥∥ 9 13
41-50 ∦∦ ∥∥ 9 22
51-60 ∦∦ ∥ 7 29
61-70 ∦∦ ∥l 8 37
71-80 ∥l 3 40



Plot the points (30,4), (40,13), (50,22), (60,29), (70,37) and (80,40) on the graph and join them with free hand to obtain an ogive.
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Question 73 Marks
Draw an ogive for each of the following distributions:
Age in years (less than) 10 20 30 40 50 60 70
Cumulative frequency 0 17 32 37 53 58 65
Answer
Age in years (less than) Cumulative Frequency
10 0
20 17
30 32
40 37
50 53
60 58
70 65


Steps of construction:
(a) Plot the points (10,8), (20, 25), (30, 38), (40, 50) and (50, 67) on the graph.
(b) Join them with free hand to obtain an ogive.
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Question 83 Marks
Draw an ogive for each of the following distributions: 
Marks obtained Less than 10 Less than 20 Less than 30 Less than 40 Less than 50
No of students 8 25 38 50 67
Answer
Marks Obtained No. of students (c.f.)
less than 10 8
less than 20 25
less than 30 38
less than 40 50
less than 50 67

Steps of construction:
(a) Plot the points (10,8), (20, 25), (30, 38), (40, 50) and (50, 67) on the graph.
(b) Join them with free hand to obtain an ogive.
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Question 93 Marks
Draw a cumulative frequency curve (ogive) for each of the following distributions: 
Class Interval 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59
Frequency 23 16 15 20 12
Answer
Class Interval (Inclusive) Class Interval (Exclusive) Frequency Cumulative Frequency
10-19 9.5-19.5 23 23
20-29 19.5-29.5 16 39
30-39 29.5-39.5 15 54
40-49 39.5-49.5 20 74
50-59 49.5-59.5 12 86
    Total 86
Steps of construction:
(a) Convert the data into exclusive form.
(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.
(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.
(d) Join the mid-points of the rectangle to obtain the ogive.
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Question 103 Marks
Draw histogram ffor the following distributtions: 
Class Marks 16 24 32 40 48 56 64
Frequency 8 12 15 18 25 19 10
Answer
Class Marks Class Intervals Frequency
16 12-20 08
24 20-28 12
32 28-36 15
40 36-44 18
48 44-52 25
56 52-60 19
64 60-68 10

Step of construction:
(a) Convert the class marks into class intervals.
(b) Taking suitables scales, marks class intervals on x-axis and frequency on y-axis
(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.
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Question 113 Marks
Draw histrogram for the following distributions:
Class interval 30-39 40-49 50-59 60-69 70-79
Frequency 24 16 09 15 20
Answer
Class Interval (Inclusive from ) Class Interval (Exclusive from) Frequency
30-39 29.5-39.5 24
40-49 39.5-49.5 16
50-59 49.5-59.5 09
60-69 59.5-69.5 15
70-79 69.5-79.5 20

Step of construction:
(a) Convert the data into exclusive form.
(b) Taking suitable scales, marks class interval on x-axis abd frequency on y-axis.
(c) Construct rectangle with class intervals as bases and corresponding frequencies as heights.
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Question 123 Marks
Draw histogram for the following distributions:
Class Interval 10-16 16-22 22-28 28-34 34-40
Frequency 15 23 30 20 16
Answer
Class Interval Frequency
10-16 15
16-22 23
22-28 30
28-34 20
34-40 16
Steps of construction:
(a)Taking suitable scales, marks class intervals on x-axis and frequency on y-axis.
(b) Construct rectangles with class intervals as bases and corresponding freqencies as heights.
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Question 133 Marks
Draw histogram for the following distributions: 
Class Interval 0-10 10-20 20-30 30-40 40-50 50-60
Frequancy 12 20 26 18 10 6
Answer
Class Interval Frequency
0-10 12
10-20 20
20-30 26
30-40 18
40-50 10
50-60 06

Step of construction :
(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.
(b) Construct rectangele with class interval as bases and corresponding frequencies as heights.
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Question 143 Marks
Construct a frequency distribution table for each of the following distributions.
Marks (more than)0102030405060708090100
Cumulative frequency100876555423631211870
Answer
Marks (more than) Cumulative frequency Frequency
0 - 10 100 13
10 - 20 87 22
20 - 30 65 10
30 - 40 55 13
40 - 50 42 6
50 - 60 36 5
60 - 70 31 10
70 - 80 21 3
80 - 90 18 11
90 - 100 7 7
Total 100
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Question 153 Marks
Construct a frequency distribution table for each of the following distributions
Marks (less than)0102030405060708090100
Cumulative frequency0728547184105147180196200
Answer
Marks (less than) Cumulative frequency Frequency
0-10 7 7
10-20 28 28-7=21
20-30 54 54-28=26
30-40 17 71-54=17
40-50 84 84-71=13
50-60 105 105-84=21
60-70 147 147-105=42
70-80 180 180-147
80-90 196 196-180=16
90-100 200 200-196=4
Total 200
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Question 163 Marks
Draw histogram ffor the following distributtions:
Class Marks 16 24 32 40 48 56 64
Frequency 8 12 15 18 25 19 10
Answer
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Question 173 Marks
Draw histrogram for the following distributions:
Class interval 30-39 40-49 50-59 60-69 70-79
Frequency 24 16 09 15 20
Answer
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[3 marks sum] - Mathematics STD 10 Questions - Vidyadip