Question

Represent the following data by a histogram and then, compute the mode.

Price of sugar per kg (in Rs)	18-20	20-22	22-24	24-26	26-28	Total
Number of weeks	4	8	22	12	6	52

Answer 1

We will represent the price of sugar per kg on the X-axis and the number of weeks on the Y-axis.
Scale :
On the X-axis:
1 big division = Rs 2
On the Y-axis:
1 big division = 2 weeks
Kink mark is being applied on the X-axis.

Now, we will draw the histogram and then find the mode through the following steps:
(i) Draw the histogram to represent the following 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 that of 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 Rs 23.

The mode can also be found using the formula shown below.
Here, L=22, f_m =22, f₁ =8, f₂ =12 , h=2


$$\begin{gathered} \mathrm{Therefore},\mathrm{mode}=L+\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h \\ =22+\left[\frac{22-8}{2\times 22-8-12}\right]\times 2 \\ =22+\frac{28}{24} \\ =\mathrm{Rs}23.17 \end{gathered}$$