Frequency Polygon

Q.

Draw a frequency polygon for the following frequency distribution:
$\begin{array}{ccccccc}\text{Class interval}& 1-10& 11-20& 21-30& 31-40& 41-50& 51-60\\ \text{Frequency}& 8& 3& 6& 12& 2& 7\end{array}$

Q.

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.

Q. What is the formula for adjusted frequency?

Q.

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

Q.

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?

Q.

In a study of diabetic patients in a village, the following observations were noted.
$\begin{array}{ccccccc}\text{Age in years}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{Number of patients}& 2& 5& 12& 19& 9& 4\end{array}$
Represent the above data by a frequency polygon.

Q.

Draw the frequency polygon representing the following frequency distribution.

$\begin{array}{ccccccc}\text{Class interval}& 30-34& 35-39& 40-44& 45-49& 50-54& 55-59\\ \text{Frequency}& 12& 16& 20& 8& 10& 4\end{array}$
[4 MARKS]

Q. Given below is a cumulative frequency distribution table showing the ages of people living in a locality:

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.

Q.

Q. The ages (in years) of 360 patients treated in a hospital on a particular dayare given below.

$\begin{array}{ccccccc}\text{Age in years}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{Number of}& & & & & & \\ \text{patients}& 90& 40& 60& 20& 120& 30\end{array}$

Draw a histogram and a frequency polygon on the same graph to represent the above data.

Q. Question 22
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

Q. Question 2
Determine the mean of the following distribution
$\begin{array}{cc}Marks& Numberofstudents\\ Below10& 5\\ Below20& 9\\ Below30& 17\\ Below40& 29\\ Below50& 45\\ Below60& 60\\ Below70& 70\\ Below80& 78\\ Below90& 83\\ Below100& 85\end{array}$

Q.

Ina frequency distribution , ogives are graphical representation of

(a) Frequency (b) Relative frequency

(c) Cumulative (d) Raw data

Q. The following is the distribution of total household expenditure (in Rs.) of manual worker in a city:

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.

Q.

Question 6
The following table gives the distribution of students of two sections according to the marks obtained by them:
$\begin{array}{cccc}\text{Section A}& & \text{Section B}& \\ \text{Marks}& \text{Frequency}& \text{Marks}& \text{Frequency}\\ 0-10& 3& 0-10& 5\\ 10-20& 9& 10-20& 19\\ 20-30& 17& 20-30& 15\\ 30-40& 12& 30-40& 10\\ 40-50& 9& 40-50& 1\end{array}$
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.

Q.

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:
$\begin{array}{cc}\text{Length (in mm)}& \text{Number of leaves}\\ 118-126& 3\\ 127-135& 5\\ 136-144& 9\\ 145-153& 12\\ 154-162& 5\\ 163-171& 4\\ 172-180& 2\end{array}$
(ii) Is there any other suitable graphical representation for the same data?

Q.

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 $Rs.850$ ?

Q.

Hi

How to find class mark for a frequency polygon.

Q.

Draw a histogram for the following data:

$\begin{array}{ccccccc}\text{Class interval}& 600-640& 640-680& 680-720& 720-760& 760-800& 800-840\\ \text{Frequency}& 18& 45& 153& 288& 171& 63\end{array}$
Using this histogram, draw the frequency polygon on the same graph

Q. Draw a histogram and the frequency polygon from the following data.

Class interval	20−25	25−30	30−35	35−40	40−45	45−50
Frequency	30	24	52	28	46	10

Q.

Make a frequency polygon from the given data.

$$\begin{array}{cc}Weight\left(kg\right)& NumberOfStudents\\ 35.5-40.5& 5\\ 40.5-45.5& 2\\ 45.5-50.5& 12\\ 50.5-55.5& 2\\ 55.5-60.5& 45\end{array}$$

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Q. A survey was conducted to know the hobby of 220 students of class IX. Out of which 130 students informed about their hobby as rock climbing and 180 students informed about their hobby as sky watching. There are 110 students who follow both the hobbies. Then how many students do not have any of the two hobbies ? How many of them follow the hobby of rock climbing only ? How many students follow the hobby of sky watching only ?

Q.

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.

1. The total number of presidents is 45.

2. The youngest president was 44 years old

3. The youngest president was 39 years old.

4. The oldest president is 74 years old.

Q.

Which of the following statements is incorrect

1. The formula for computing the adjusted frequencies is {Maximum class size /class mark} x frequency of the class

2. For drawing a histogram of a continuous grouped frequency distribution with unequal class intervals, you have to compute the adjusted frequencies of each class

3. For a given frequency distribution, a frequency polygon can be drawn without using a histogram

4. To construct a histogram, you have to construct rectangles with class intervals as bases and respective frequencies as heights

Q. The daily earnings of 30 workers are given below:

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.

Q.

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

1. (i) 246 (ii) 4-7

2. (i) 103 (ii) 7-10

3. (i) 140 (ii) 10-13

4. (i) 85 (ii) 4-7

Q. Construct a frequency polygon with the help of histogram for the given data :

$\begin{array}{cccccc}\text{Classes}& \text{0-6}& \text{6-12}& \text{12-18}& \text{18-24}& \text{24-30}\\ \text{Frequencies}& \text{4}& \text{8}& \text{15}& \text{20}& \text{6}\end{array}$

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3. 

Q.

A coin is tossed twice. If the second throw results in head, then a die is thrown. Describe the sample space of the experiment.

Q.

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

1. True

2. False

Q.

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.