1. **State the problem:** We have age groups of employees and their frequencies. We need to draw a frequency polygon, frequency curve, and histogram with frequency polygon on the same graph. 2. **Calculate midpoints for each age group:** - For 16-20: midpoint $= \frac{16+20}{2} = 18$ - For 21-25: midpoint $= \frac{21+25}{2} = 23$ - For 26-30: midpoint $= \frac{26+30}{2} = 28$ - For 31-35: midpoint $= \frac{31+35}{2} = 33$ - For 36-40: midpoint $= \frac{36+40}{2} = 38$ 3. **Frequency data:** - 16-20: 10 - 21-25: 18 - 26-30: 24 - 31-35: 12 - 36-40: 6 4. **Draw frequency polygon:** - Plot points at midpoints vs frequency: $(18,10), (23,18), (28,24), (33,12), (38,6)$ - Connect these points with straight lines. - To close the polygon, add points at the start and end with frequency zero: - Before 16-20 midpoint: $13$ (midpoint of 11-15) with frequency 0 - After 36-40 midpoint: $43$ (midpoint of 41-45) with frequency 0 - So points for polygon: $(13,0), (18,10), (23,18), (28,24), (33,12), (38,6), (43,0)$ 5. **Draw frequency curve:** - Smooth curve passing through the same points as the frequency polygon. 6. **Draw histogram:** - Draw bars for each class interval with height equal to frequency. - Width of each bar corresponds to class width (5 years). 7. **Draw frequency polygon on same graph as histogram:** - Plot the polygon points on top of histogram bars and connect with lines. This completes the graphical representation of the data. Final answer: Frequency polygon points are midpoints with frequencies connected by lines including zero frequency points at start and end.