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Mathematics [4 marks sum]

Graphical Representations · ICSE STD 10 (ICSE - English Medium). 18 questions.

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[4 marks sum]

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18 questions · timed · auto-graded

Question 14 Marks
Construct histograms for following frequency distribution:
Class Mark15253545505560
Frenuencv6121518251410
Answer
Steps:
a. Make the class intervals continuous by taking class mark as midpoints.
b. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
c. On the y-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
d. Draw rectangles of histogram as per given data.
Class IntervalFrequency
0-9.5-
9.5-19.56
19.5-29.512
29.5-39.515
39.5-47.518
47.5-52.525
52.5-57.514
57.5-62.510
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Question 24 Marks
Draw an ogive for the following :
Marks (More than)0102030405060708090100
Cumulative Frequency100876555423631211870
Answer
Steps:
1. Start with lower limits of class intervals and from cumulative frequency, subtract the frequency of each class to obtain c.f distribution .
2. Mark lower class limits along $x$-axis $.1 \mathrm{~cm}=5$ units
3. Mark cumulative frequencies along y-axis. $1 \mathrm{~cm}=5$ units
4. Plot points $(x, f)$ where $x$ is the lower limit of one class and $f$ is the corresponding c.f. $(0,100),(10,87)$, $(20,65),(30,55),(40,42),(50,36),(60,31),(70,21),(80,18),(90,7),(100,0)$
5. Join the points to get the ogive.
Marks more thanCumulative Frequency
0100
1087
2065
3055
4042
5036
6031
7021
8018
907
1000
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Question 34 Marks
Draw an ogive for the following :
Marks obtainedMore than 10More than 20More than 30More than 40More than 50
No. of students825385067
Answer
Steps:
1. Start with lower limits of class intervals and from cumulative frequency, subtract the frequency of each class to obtain c.f distribution.
2. Mark lower class limits along $x$-axis. $1 \mathrm{~cm}=5$ units
3. Mark cumulative frequencies along y-axis. $1 \mathrm{~cm}=5$ units
4. Plot points $(x, f)$ where $x$ is the lower limit of one class and $f$ is the corresponding c.f. $(10,188)$, $(20,180),(30,155),(40,117),(50,67)$
5. Join the points to get the ogive.
Marks more thanFrequencyCumulative Frequency
108188
2025180
3038155
4050117
506767
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Question 44 Marks
Draw an ogive for the following :
Age in yearsLess than 10Less than 20Less than 30Less than 40Less than 50
No. of people0174267100
Answer
Steps :
1. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot age .
2. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
3. Plot the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequecies . In this case $(10,0),(20,17),(30,42),(40,67),(50,100)$.
4. Join the points plotted by a smooth curve.
Age less thanCumulative Frequency
100
2017
3042
4067
50100
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Question 54 Marks
Draw an ogive for the following :
Marks obtainedLess than 10Less than 20Less than 30Less than 40Less than 50
No. of students822486075
Answer
Steps :
1. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot marks.
2. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
3. Plot the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies . In this case $(10,8),(20,22),(30,48),(40,60),(50,75)$.
4. Join the points plotted by a smooth curve.
Marks less thanCumulative Frequency
108
2022
3048
4060
5075
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Question 64 Marks
Draw an ogive for the following :
Class Interval10-1920-2930-3940-4950-59
Frequency2823152014
Answer
Steps:
1. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
2. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
3. Plot the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies . In this case $(19,28),(29,51),(39,66),(49,86),(59,100)$.
4. Join the points plotted by a smooth curve.
less thanCumulative Frequency
1928
2951
3966
4986
59100
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Question 74 Marks
Draw an ogive for the following :
Class Interval100-150150-200200-250250-300300-350350-400
Frequency10131712108
Answer
Steps :
1. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
2. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
3. plot the points with coordinates having abscissae as actual limits and ordinates as the cumulative frequencies . In this case $(150,10),(200,23),(250,40)(300,52)(350,62),(400,70)$.
4. Join the points plotted by a smooth curve.
less thanCumulative Frequency
15010
20023
25040
30052
35062
40070

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Question 84 Marks
Construct a frequency polygon without using a histogram for the following frequency distribution :
Class Interval 1-10 11-20 21-30 31-40 41-50
Frequency 8 12 10 16 6
Answer
Steps:
1. Make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.
2. Find class mark by calculating the average of the class interval.
3. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
4. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
5. Plot the points on the graph. $(5.5,8),(15.5,12),(25.5,10),(35.5,16),(45.5,6)$.
6. Mark two more midpoints of zero frequency on $x$-axis at the start and at the end.
7. Now connect the points using straight lines.
Class IntervalClass MarkFrequency
0.5-10.5$
=\frac{0.5+10.5}{2}=5.5
$		8
10.5-20.5$
=\frac{10.5+20.5}{2}=15.5
$		12
20.5-30.5$
=\frac{20.5+30.5}{2}=25.5
$		10
30.5-40.5$
=\frac{30.5+40.5}{2}=35.5
$		16
40.5-50.5$
=\frac{40.5+50.5}{2}=45.5
$		6
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Question 94 Marks
Construct a frequency polygon without using a histogram for the following frequency distribution :
Class Interval10-2020-4040-6060-8080-100
Frequency917152014
Answer
Steps:
1. Find class mark by calculating the average of the class interval.
2. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
3. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
4. plot the points on the graph. $(15,9),(30,17),(50,15),(70,20),(90,14)$.
5. Mark two more midpoints of zero frequency on $x$-axis at the start and at the end .
6. Now connect the points using staright lines.
Class IntervalClass markFrequency
10-20$
=\frac{10+20}{2}=15
$		9
20-40$
=\frac{20+40}{2}=30
$		17
40-60$
=\frac{40+60}{2}=50
$		15
60-80$
=\frac{60+80}{2}=70
$		20
80-100$
=\frac{80+100}{2}=90
$		14
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Question 104 Marks
Construct a frequency polygon without using a histogram for the following frequency distribution :
Class Mark10152025303540
Frequency420404530255
Answer
Steps:
1. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
2. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
3. Mark the given data on the graph. $(10,4),(15,20),(20,40),(25,45),(30,30),(35,25),(40,5)$
4. Mark two more midpoints of zero frequency on $x$-axis at the start and at the end.
5. Now connect the points using staright lines.
Class MarkFrequency
104
1520
2040
2545
3030
3525
405
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Question 114 Marks
Construct a histogram and then a frequency polygon for the following frequency distribution.
Class Interval100-150150-200200-250250-300300-350
Frequency1015171210
Answer
Steps :
1. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
2. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency .
3. Draw rectangles of histogram as per given data .
4. For each rectangle, mark the midpoint of its length at the top part. In this case, points are $(125.10),(175,15),(225,17),(275,12),(325,10)$.
5. Mark two more midpoints of Zero frequency on $x$-axis at the start and at th end.
6. Now connect the points using straight lines.
Class Interval Frequency
100-15010
150-20015
200-25017
250-30012
300-35010
Image
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Question 124 Marks
Construct a histogram and then a frequency polygon for the following frequency distribution.
Class Interval11-2021-3031-4041-5051-6061-70
Frequency152850352012
Answer
1. Organize the data into equal intervals by subtracting 0.5 from lower limit of each class and add 0.5 to the upper limit of each class .
2. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval .
3. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
4. Draw rectangles of histogram as per given data.
5. For each rectangle, mark the midpoint of its length at the top part . In this case, points are $(15.5,15),(25.5,28),(35.5,50),(45.5,35),(55.5,20),(65.5,12)$.
6. Mark two more midpoints of zero frequency on $x$-axis at the start and at the end .
7. Now connect the points using straight lines.
Class Interval Frequency
10.5-20.515
20.5-30.528
30.5-40.550
40.5-50.535
50.5-60.520
60.5-70.512
Image
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Question 134 Marks
Construct a histogram and then a frequency polygon for the following frequency distribution.
Class Interval0-1010-2020-3030-4040-5050-60
Frequency8132735143
Answer
Steps:
1. On the $x$-axis , take $1 \mathrm{~cm}$ as 5 units and plot class interval.
2. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
3. Draw rectangle of histogram as per given data.
4. For each rectangle, mark the midpoint of its length at the top part . In this case, points are $(5,8)$, $(15,13),(25,27),(35,35),(45,14),(55,3)$.
5. Mark two more midpoints of zero frequency on $x$-axis at the start and at the end.
6. Now connect the points using straight lines.
Class IntervalFrequency
0-108
10-2013
20-3027
30-4035
40-5014
50-603
Image
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Question 154 Marks
Construct histograms for following frequency distribution:
Class Interval110-119120-129130-139140-149150-159
Frequency1523302016
Answer
Steps:
a. Make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.
b. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class intervals.
c. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
d. Draw rectangles of histogram as per given data.
Class IntervalFrequency
109.5-119.515
119.5-129.523
129.5-139.530
139.5-149.520
149.5-159.516
Image
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Question 164 Marks
Construct histograms for following frequency distribution:
Class Interval1-1011-2021-3031-4041-50
Frequency1123302016
Answer
Steps :
a. Make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class .
b. On the $x$-axis, take $1 \mathrm{~cm}$ as 5 units and plot class interval.
c. On the $y$-axis, take $1 \mathrm{~cm}$ as 5 units and plot frequency.
d. Draw rectangles of histogram as per given data.
Class IntervalFrequency
0.5-10.511
10.5-20.523
20.5-30.530
30.5-40.520
40.5-50.516
Image
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[4 marks sum] - Mathematics STD 10 Questions - Vidyadip