Frequency Polygon
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Draw a frequency polygon for the following frequency distribution:
Class interval1−1011−2021−3031−4041−5051−60Frequency8361227
The following table gives the distribution of students of two sections according to the mark obtained by them:
Section A |
Section B |
||
Marks |
Frequency |
Marks |
Frequency |
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 |
3 9 17 12 9 |
0 − 10 10 − 20 20 − 30 30 − 40 40 − 50 |
5 19 15 10 1 |
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.
A frequency polygon is constructed by plotting frequency of the class interval and the
(a) Upper limit of the class
(b) Lower limit of the class
(c) mid value of the class
(d) any values of the class
The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:
Length (in mm) | Number of leaves |
118 − 126 127 − 135 136 − 144 145 − 153 154 − 162 163 − 171 172 − 180 | 3 5 9 12 5 4 2 |
(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 to conclude that the maximum number of leaves are 153 mm long? Why?
In a study of diabetic patients in a village, the following observations were noted.
Age in years10−2020−3030−4040−5050−6060−70Number of patients25121994
Represent the above data by a frequency polygon.
Draw the frequency polygon representing the following frequency distribution.
Class interval30−3435−3940−4445−4950−5455−59Frequency1216208104
[4 MARKS]
Age in years | No. of persons |
Above 108 Above 96 Above 84 Above 72 Above 60 Above 48 Above 36 Above 24 Above 12 Above 0 |
0 1 3 5 20 158 427 809 1026 1124 |
Prepare a frequency distribution table.
Age in years10−2020−3030−4040−5050−6060−70Number ofpatients9040602012030
Draw a histogram and a frequency polygon on the same graph to represent the above data.
For drawing a frequency polygon of a continuous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abcissae are, respectively:
A) Upper limits of the classes
B) Lower limits of the classes
C) Class marks of the classes
D) Upper limits of preceding classes
Determine the mean of the following distribution
MarksNumber of studentsBelow 10 5Below 20 9Below 30 17Below 40 29Below 50 45Below 60 60Below 70 70Below 80 78Below 90 83Below 100 85
Ina frequency distribution , ogives are graphical representation of
(a) Frequency (b) Relative frequency
(c) Cumulative (d) Raw data
Expenditure (in Rs): |
100-150 | 150-200 | 200-250 | 250-300 | 300-350 | 350-400 | 400-450 | 450-500 |
No. of manual workers: | 25 | 40 | 33 | 28 | 30 | 22 | 16 | 8 |
Draw a histogram and a frequency polygon representing the above data.
Question 6
The following table gives the distribution of students of two sections according to the marks obtained by them:
Section ASection BMarksFrequencyMarksFrequency0−1030−10510−20910−201920−301720−301530−401230−401040−50940−501
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.
Question 4 (ii)
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 leaves118−1263127−1355136−1449145−15312154−1625163−1714172−1802
(ii) Is there any other suitable graphical representation for the same data?
Draw a histogram for the frequency table made for the data in Question 3 and answer the following questions. (i) Which group has the maximum number of workers? (ii) How many workers earn $Rs.850$and more? (iii) How many workers earn less than $Rs.850$ ?
Hi
How to find class mark for a frequency polygon.
Draw a histogram for the following data:
Class interval600−640640−680680−720720−760760−800800−840Frequency184515328817163
Using this histogram, draw the frequency polygon on the same graph
Class interval | 20−25 | 25−30 | 30−35 | 35−40 | 40−45 | 45−50 |
Frequency | 30 | 24 | 52 | 28 | 46 | 10 |
Make a frequency polygon from the given data.
Weight(kg)NumberOfStudents35.5−40.5540.5−45.5245.5−50.51250.5−55.5255.5−60.545
The graph below shows the ages of presidents of a country at the time of inauguration or start of their tenure.
Find the correct option(s) among the following.
The total number of presidents is 45.
The youngest president was 44 years old
The youngest president was 39 years old.
The oldest president is 74 years old.
Which of the following statements is incorrect
The formula for computing the adjusted frequencies is {Maximum class size /class mark} x frequency of the class
For drawing a histogram of a continuous grouped frequency distribution with unequal class intervals, you have to compute the adjusted frequencies of each class
For a given frequency distribution, a frequency polygon can be drawn without using a histogram
To construct a histogram, you have to construct rectangles with class intervals as bases and respective frequencies as heights
Daily earning (in ₹) | No. of workers |
1-50 | 3 |
50-100 | 7 |
100-150 | 4 |
150-200 | 5 |
200-250 | 4 |
250-300 | 3 |
300-350 | 2 |
350-400 | 2 |
Draw a histogram and a frequency polygon to represent the above data.
Given below is age group of different children and Cumulative Frequency
Below 4 0
Below 7 85
Below 10 140
Below 13 243
Below 16 300
Find the number of children in the age of 10 -13
Which of the age group had least number of Children
(i) 246 (ii) 4-7
(i) 103 (ii) 7-10
(i) 140 (ii) 10-13
(i) 85 (ii) 4-7
Classes0-66-1212-1818-2424-30Frequencies4815206
A coin is tossed twice. If the second throw results in head, then a die is thrown. Describe the sample space of the experiment.
To complete the frequency polygon plot we assume a class interval with frequency zero and add one before and one after the given class intervals
True
False
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.