Question

The length of 40 leaves of a plant is measured correct to one millimeter 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	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?

Answer 1

(i) Let us find half the difference between lower limit of a class and upper limit of its preceding class to make the continuous distribution. 

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

Representation of given data in the form of a histogram is as follows:

Length of 40 leaves of a plant measured correct to one millimeter. Scale chosen: On y-axis – 1 large division, i.e. 1 cm = 1 leave

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(ii) Yes, we can represent the given data by other graphical representation named as Frequency Polygon which is as follows:
 

Length in mm	Class mark	Number of leaves
117.5-126.5	122	3
126.5-135.5	131	5
135.5-144.5	140	9
144.5-153.5	149	12
153.5-162.5	158	5
162.5-171.5	167	4
171.5-180.5	176	2

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(iii) No, because the maximum number 12 is corresponding to the class interval 145 -153 which implies that the leaves whose length are 145 mm or less than 153 mm are maximum in number.