The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:
(i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
(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?
Solution:
(i) From the given data, we can observe that the length of leaves is given in discontinuous class intervals, having a difference of 1 unit in between each
For making the class intervals continuous, we will do the following:
We have to find the difference between the upper limit and the lower limit of a class. We then add half of the resultant difference to each upper limits and subtract the same resultant difference from each of the lower limits. Since the difference between the upper limit and the lower limit of a class is 1 i.e, (127 – 126 = 1). So half of 1 is 0.5.
Now the frequency distribution table is given below.
Length (in mm) |
Number of Leaves |
117.5–126.5 |
3 |
126.5–135.5 |
5 |
135.5–144.5 |
9 |
144.5–153.5 |
12 |
153.5–162.5 |
5 |
162.5–171.5 |
4 |
171.5–180.5 |
2 |
The above data is represented through a histogram as below:
- Represent length of leaves on the x-axis (in mm) and the number of leaves on the y-axis.
- Put a scale of ‘1 unit = 2 leaves on y-axis since the lower-class value is 2 and the highest class value is 12.
- Also, since the interval of first-class is starting from 117.5 and not from zero, we represent it on the graph by making a kink on the x-axis.
- Now draw rectangular bars of equal width and the lengths according to the class interval's frequencies.
(ii) The other suitable graphical representation of the given data would be a frequency polygon.
(iii) The maximum number of leaves lie between 144.5 mm and 153.5 mm in length. Hence, we can't conclude that the maximum leaves are 153 mm long.
Video Solution:
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: (i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous] ii) Is there any other suitable graphical representation for the same data? iii) Is it correct to conclude that the maximum number of leaves is 153 mm long? Why?
NCERT Solutions for Class 9 Maths - Chapter 14 Exercise 14.3 Question 4:
Summary:
The length of 40 leaves of a plant is measured correct to one millimetre, and the obtained data is represented in the histogram. The other suitable graphical representation of the given data would be a frequency polygon. We have found that the maximum number of leaves has their length lie between 144.5 mm and 153.5 mm. Hence, we can't conclude that the maximum leaves are 153 mm long.