Question

An automatic filling machine was tested for its performance. The data of a sample of 100 filled packets is classified as shown.

Weight (in gm )	485-490	490-495	495-500	500-505	505-510	510-515
No. of packets	12	18	20	22	24	4

Draw a histogram and find the mode of the weight of packets.

Answer 1

(i) Draw a 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 of the pre-modal class (A) by a straight line .
(iv) Join the left-hand top vertices of modal class (B) and of the 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.



We can also verify it by using the formula for calculating mode.
Here, L = 505, f_m = 24, f₁ = 22, f₂ = 4 , h = 5

$$\begin{gathered} \mathrm{Therefore},\mathrm{mode}=L+\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h \\ =505+\left[\frac{24-22}{2\times 24-22-4}\right]\times 5 \\ =505+\frac{10}{22} \\ =505.45 \end{gathered}$$