The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:

 

S.No.	Length (in mm)	Number of leaves
1.	118 – 126	3
2.	127 – 135	5
3.	136 – 144	9
4.	145 – 153	12
5.	154 – 162	5
6.	163 – 171	4
7.	172 – 180	2

(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) The data given in the question is represented in discontinuous class interval. So, we have to make it in continuous class interval. The difference is 1, so taking half of 1, we subtract ½ = 0.5 from lower limit and add 0.5 to the upper limit. Then the table becomes:

S.No.	Length (in mm)	Number of leaves
1.	117.5 – 126.5	3
2.	126.5 – 135.5	5
3.	135.5 – 144.5	9
4.	144.5 – 153.5	12
5.	153.5 – 162.5	5
6.	162.5 – 171.5	4
7.	171.5 – 180.5	2

(ii) Yes, the data given in the question can also be represented by frequency polygon.

(iii) No, we cannot conclude that the maximum number of leaves are 153 mm long because the maximum number of leaves are lying in-between the length of 144.5 – 153.5