Question

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

Length (in mm)	Number of leaves
118 − 126 127 − 135 136 − 144 145 − 153 154 − 162 163 − 171 172 − 180	3 5 9 12 5 4 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) It can be observed that the length of leaves is represented in a discontinuous class interval having a difference of $1$ in between them. Therefore, has to be added to each upper class limit and subtracted from each lower class limits so as to make the class intervals continuous.

Thus,

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

Since, the class intervals are continuous now, can construct the histogram of the given frequency table.

Taking the length of leaves on $x$-axis and the number of leaves on $y$-axis, the histogram of this information can be drawn as above.

Here, 1 unit on $y$-axis represents $2$ leaves.

(ii) Other suitable graphical representation of this data is frequency polygon as that also helps to represent the continuous frequency distribution table/data.

(iii) No, as maximum number of leaves (i.e., $12$) has their length in between $144.5$ mm and $153.5$ mm. It is not necessary that all have their lengths as $153$ mm.