The length of 40 leaves of a plant are measured correct to one millimetre, 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. [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?
First we convert the discontinuous classes into continuous classes because the upper limit of the first interval does not match the lower limit of the second interval.
By formula,
Adjustment factor
=
Substituting values we get :
Adjustment factor: = = 0.5
So, 0.5 has to be added to each upper class limits and subtracted from each lower class limits to make the class interval continuous.
| Length (in mm) | Classes | 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 |
Since, the class intervals are continuous, now we can construct the histogram of the given frequency table.
(i) Steps of construction of histogram :
Plot the classes of leaves on x-axis.
Plot number of leaves on y-axis by taking 1 unit = 2 leaves.
Since, the scale on x-axis starts at 117.5, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 117.5.
We draw rectangular bars of equal width and the lengths according to the class interval's frequencies.
(ii) Frequency polygon is another suitable graphical representation for the same data.
(iii) The maximum number of leaves lie between 144.5 mm - 153.5 mm in length, which is a range.
No, we can't conclude that the maximum leaves are 153 mm long.