Question

Draw the histogram to represent the following data and then, find the mode .

Daily sales of a store (in Rs)	0-1000	1000-2000	2000-3000	3000-4000	4000-5000	Total
Number of days in a month	2	12	10	4	2	30

Answer 1

We will draw the daily sales of the store on the X-axis and the number of days in a month on the Y-axis.
We have chosen the following scale for this purpose.
On the X -axis:
1 big division = Rs 1000
On the Y- axis:
1 big division = 2 days
We will find the mode from the graph with the following steps.
(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 the modal class (C) and pre-modal class (a) by a straight line .
(iv) Join the left-hand top vertices of the 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 the mode is Rs 1800.

The mode can also be calculated by using the standard formula.
Here, L=1000, f_m =12, f₁ =2, f₂ =10 , h=1000


$$\begin{gathered} \mathrm{Therefore},\mathrm{mode}=L+\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h \\ =1000+\left[\frac{12-2}{2\times 12-2-10}\right]\times 1000 \\ =1000+\frac{10000}{12} \\ =\mathrm{Rs}.1833.33 \end{gathered}$$