Question

Draw the histogram, frequency curve and frequency polygon for the data given below.

Class intervals	5-10	10-15	15-20	20-25	25-30
Frequency	4	6	3	2	1

Also, find the mode graphically.

Answer 1

(i) Draw the histogram to represent the data.
(ii) Locate the modal class, pre-modal class and post-modal class.
(iii) Join the right-hand top vertices of modal class (C) and pre-modal class (A) by a straight line.
(iv) Join the left-hand top vertices of modal class (B) and post-modal class (D) by a straight line.
(v) Let the point of intersection of AC and BD be E.
(vi) Draw a segment EF perpendicular to the X-axis.
(vii) The foot of the perpendicular, F, is the mode.

Here is the histogram showing the mode graphically.




From the graph we find that the value of mode is 12.
We can verifythe mode by using the formula also.
Here, L = 10, f_m = 6, f₁ = 4, f₂ = 3 , h = 5


$$\begin{gathered} \mathrm{Therefore},\mathrm{mode}=L+\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h \\ =10+\left[\frac{6-4}{2\times 6-4-3}\right]\times 5 \\ =10+\frac{10}{5} \\ =12 \end{gathered}$$

Class mark	2.5	7.5	12.5	17.5	22.5	27.5	32.5
Frequency	0	4	6	3	2	1	0

The frequency polygon is shown below.



The frequency curve is shown below.