Question

Show the following data by a frequency polygon:
\[ \begin{array}{|c|c|} \hline \text{Electricity Bill (₹)} & \text{Families (f)} \\ \hline 200 - 400 & 240 \\ 400 - 600 & 300 \\ 600 - 800 & 450 \\ 800 - 1000 & 350 \\ 1000 - 1200 & 160 \\ \hline \end{array} \]

Hint:

A frequency polygon can be obtained by joining the mid-points of histogram rectangles, or directly by plotting class mid-points versus frequencies.

Answer 1

Step 1: Find the class mid-points.
\[ \text{Mid-point (x)} = \frac{\text{Upper class limit} + \text{Lower class limit}}{2} \] \[ \begin{array}{|c|c|c|} \hline \text{Class Interval} & \text{Mid-point (x)} & \text{Frequency (f)} \\ \hline 200 - 400 & 300 & 240 \\ 400 - 600 & 500 & 300 \\ 600 - 800 & 700 & 450 \\ 800 - 1000 & 900 & 350 \\ 1000 - 1200 & 1100 & 160 \\ \hline \end{array} \] Step 2: Plot the points.
On a graph paper: - Take class mid-points (x) on the X-axis. - Take frequencies (f) on the Y-axis. - Plot the points: \[ (300, 240), (500, 300), (700, 450), (900, 350), (1100, 160) \] Step 3: Join these points by straight lines.
To complete the polygon, join the first point to the previous mid-point (100, 0) and the last point to the next mid-point (1300, 0). Step 4: Conclusion.
The resulting closed figure represents the Frequency Polygon for the given data.
Final Answer: \[ \boxed{\text{Frequency Polygon drawn with mid-points } (300, 500, 700, 900, 1100)} \]