Question

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 153mm long? Why?

Length in mm	Number of leaves
118-126	3
127-135	5
136-144	9
145-153	12
154-162	5
163-172	4
172-180	2

Answer 1

Hint: Before starting with graphical representation, we should convert the discontinuous classes into continuous class, as they have asked for a histogram. Then, we shall choose the axis of the graph, by taking the number of leaves as y-axis and length of the leaf on x-axis.

Complete step-by-step answer:
The Difference Between Bar Charts and Histograms
With bar charts, each column represents a group defined by a categorical variable; and with histograms, each column represents a group defined by a continuous, quantitative variable.

We shall first convert the discontinuous classes into continuous classes.
In order to do so consider
\[{\text{Adjustment }} = {\text{ }}\dfrac{1}{2}{\text{[lower limit class - upper limit of previous]}}\]
So, we get adjustment: $ = \dfrac{1}{2}[127 - 126] = \dfrac{1}{2} = 0.5 $
Therefore, subtract 0.5 from upper limit of previous class & lower limit of next class.

Length in mm	New Length in mm	Number of leaves
118-126	117.5-126.5	3
127-135	126.5-135.5	5
136-144	135.5-144.5	9
145-153	144.5-153.5	12
154-162	153.5-162.5	5
163-171	162.5-171.5	4
172-180	171.5-180.5	2

i.Now, to draw the histogram we choose number of leaves on Y-axis and length on X-axis

ii.Yes we can also represent it through frequency polygon.

iii.No, we cannot conclude that, maximum number of leaves is 153 mm. It is a range. We can say that, maximum number of leaves lies between 144.5mm - 153.5 mm.

Note: Remember that in order to draw a histogram, there should be continuous class intervals. Otherwise, we cannot draw a histogram.so convent the discontinuous class interval to continuous class and then start the graphical representation.