RD Sharma Solutions for Class 9 Maths Chapter 3 Graphical Representation of Statistical Data Exercise 23.3 will help you to understand the steps involved in representing a large amount of statistical data in graphs from the very beginning. In this exercise of RD Sharma Solutions Class 9, students will learn about the construction of the histogram of a continuous grouped frequency distribution with unequal class intervals and more.
RD Sharma Solutions for Class 9 Maths Chapter 23 Graphical Representation of Statistical Data Exercise 23.3
Access Answers to RD Sharma Solutions for Class 9 Maths Chapter 23 Graphical Representation of Statistical Data Exercise 23.3 Page Number 23.41
Question 1: Construct a histogram for the following data:
Solution:
Let us consider that the horizontal and vertical axes represent the monthly school fees and the number of schools, respectively. Construct rectangles with class intervals as bases and respective frequencies as heights as below.
Histogram:
Question 2: The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on the same axes.
Solution:
Let us consider that the horizontal and vertical axes represent the height (in cm) and the number of children, respectively. Construct rectangles with class intervals as bases and respective frequencies as heights as below.
Question 3: The time taken in seconds to solve a problem by each of 25 pupils is as follows:
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20
(a) Construct a frequency distribution for these data using a class interval of 10 seconds.
(b) Draw a histogram to represent the frequency distribution.
Solution:
Arrange raw data into ascending order:
16, 20, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 52, 53, 58, 59, 60, 64
(a) Frequency distribution for the given data, using a class interval of 10 seconds.
| Class Interval | Frequency | |
| 10-20 | 16 | 1 |
| 20-30 | 20, 20, 26, 27, 28 | 5 |
| 30-40 | 30, 33, 37, 38 | 4 |
| 40-50 | 40, 42, 43, 46, 46, 46, 48, 49 | 8 |
| 50-60 | 50, 52, 53, 58, 59 | 5 |
| 60-70 | 60, 64 | 2 |
(b)
Consider horizontal and vertical axes represent the seconds and frequency, respectively. Frequencies are the heights of rectangles.
Question 4: Draw, in the same diagram, a histogram and a frequency polygon to represent the following data which shows the monthly cost of living index of a city in a period of 2 years:
Solution:
Consider the horizontal axis as the cost of living (in Rs.), and the vertical axis represents the number of months.
Histogram and a frequency polygon:
RD Sharma Solutions for Class 9 Maths Chapter 23 Graphical Representation of Statistical Data Exercise 23.3
RD Sharma Solutions Class 9 Maths Chapter 23 Graphical Representation of Statistical Data Exercise 23.3 are based on the following topics:
- Histogram
- Construction of a histogram of a continuous grouped frequency distribution with unequal class intervals
- Construction of a histogram when mid-points of class intervals are given
- Construction of a histogram when class intervals are given in the inclusive form
- Frequency polygon and its algorithm
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