Question

The salary per month of the workers in a factory were as follows:
$\begin{array}{cc}Salary\left(inRs\right)& No.ofworkers\\ 300-400& 52\\ 400-500& 43\\ 500-600& 84\\ 600-700& 142\\ 700-800& 93\\ 800-900& 62\end{array}$
i) Find the modal class of this grouped data
ii) Draw the histogram and locate the mode. [6 MARKS]

Answer 1

Part (i) : 2 Marks
Part(ii) : Histogram: 2 Marks
Mode: 2 Marks

(i) From the given grouped data, it is obvious that the class 600-700 has the maximum frequency, 142. So, 600 - 700 is the modal class of the data.

(ii) In the given frequency distribution, the first class interval is 300 - 400, so the scale on x-axis starts at 300. For this, a zig-zag curve is drawn near the origin to show that the graph to scale beginning . at 300 and not at the origin itself. Taking class interval as bases and the corresponding frequencies as heights, construct rectangles to obtain the histogram of the frequency distribution of the given grouped data.

The mode is the point of intersection of crossed' lines from the corners of the rectangles on the either of the highest rectangle to the opposite corners of the highest rectangle. Inside the highest rectangle which represents the maximum frequency, draw two lines AC and BD diagonally to the upper corners C and D of adjacent rectangles respectively. From this point of intersection P, a perpendicular PQ is drawn to x-axis. The value of point Q (i.e. 655) on the x-axis represents the value of mode. Hence, the mode is 655.