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?

Answer 1

Length (in mm)	New length (in mm)	No. 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

In order to make a histogram, we need to convert discontinuous classes to continuous classes.

Adjustment $=\frac{1}{2}(\text{lower limit of class - upper limit of previous class)}$

$=\frac{1}{2}(127-126)=0.5$

So, $0.5$ needs to be subtracted from upper limit of previous class and lower limit of next class.

(ii) Frequency polygon
(iii) No. It is a range. The maximum number of leaves lies in between $144.5mm-154.5mm$. Not necessary that it all occurs as $153mm$ length.