मराठी

Construct a Combined Histogram and Frequency Polygon for the Following Frequency Distribution: - Mathematics

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प्रश्न

Construct a combined histogram and frequency polygon for the following frequency distribution:

Class-Intervals 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60
Frequency 3 5 6 4 2
आलेख
बेरीज
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उत्तर

Steps:

1. Draw a histogram for the given data.

2. Mark the mid-point at the top of each rectangle of the histogram drawn.

3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.

4. Join the consecutive mid-point marked by straight lines to obtain the required frequency polygon.

5. The require combined histogram and frequency polygon are shown in the following figure:

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पाठ 18: Statistics - Exercise 18 (B) [पृष्ठ २३३]

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सेलिना Concise Mathematics [English] Class 9 ICSE
पाठ 18 Statistics
Exercise 18 (B) | Q 2 | पृष्ठ २३३

संबंधित प्रश्‍न

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 leaves
118 - 126 3
127 - 135 5
136 - 144 9
145 - 153 12
154 - 162 5
163 - 171 4
172 - 180
  1. Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
  2. Is there any other suitable graphical representation for the same data?
  3. Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

The following bar graph (Fig. 23. 1 4) represents the heights (in cm) of 50 students of Class XI of a particular school. Study the graph and answer the following questions:

(i) What percentage of the total number of students have their heights more than 149cm?
(ii) How many students in the class are in the range of maximum height of the class?
(iii) The school wants to provide a particular type of tonic to each student below the height
of 150 cm to improve his height. If the cost of the tonic for each student comes out to be Rs. 55, how much amount of money is required?
(iv) How many students are in the range of shortest height of the class?
(v) State whether true or false:
a. There are 9 students in the class whose heights are in the range of 155 - 159 cm.
b. Maximum height (in cm) of a student in the class is 17.
c. There are 29 students in the class whose heights are in the range of 145- 154 cm.
d. Minimum height (in cm) of a student is the class is in the range of 140 – 144 cms.
e. The number of students in the class having their heights less than 150 cm is 12.
f. There are 14 students each of whom has height more than 154. cm.


The following table gives the route length (in thousand kilometres) of the Indian Railways in some of the years:

Year 1960-61 1970-71 1980-81 1990-91 2000-2001
Route length
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56 60 61 74 98

Represent the above data with the help of a bar graph.


The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years:

Years 1982 1983-1984 1984-1985 1985-1986 1986-1987
Value of Export
of Cotton Textiles
(in crores of rupees)
300 325 475 450 550

Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.


In a frequency distribution, ogives are graphical representation of


Construct a frequency polygon for the following data:

Class-Intervals 10-14 15-19 20-24 25-29 30-34
Frequency 5 8 12 9 4

Harmeet earns Rs.50 000 per month. He a budget for his salary as per the following table:

Expenses Accommodation Food Clothing Travel Miscellaneous saving
Amount (Rs.) 12000 9000 2500 7500 4000 15000

Draw a bar graph for the above data.


The number of students (boys and girls) of class IX participating in different activities during their annual day function is given below:

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Boys 12 5 4 4 10 2
Girls 10 8 6 3 9 1

Draw a double bar graph for the above data.


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46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44

Which ‘average’ will be a good representative of the above data and why?


Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:

Class interval (km/h) Frequency
30 – 40 3
40 – 50 6
50 – 60 25
60 – 70 65
70 – 80 50
80 – 90 28
90 – 100 14

Draw the frequency polygon representing the above data without drawing the histogram.


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