To draw the histogram for this data, we first need to calculate the frequency density for each group. Frequency density is given by the formula:

$\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}$

We can calculate the frequency density for each class of heights:

1. For $0 < h \leq 20$:

   • Frequency = 15
   • Class width = $20 - 0 = 20$
   • Frequency density = $\frac{15}{20} = 0.75$

2. For $20 < h \leq 35$:

   • Frequency = 48
   • Class width = $35 - 20 = 15$
   • Frequency density = $\frac{48}{15} = 3.2$

3. For $35 < h \leq 40$:

   • Frequency = 21
   • Class width = $40 - 35 = 5$
   • Frequency density = $\frac{21}{5} = 4.2$

4. For $40 < h \leq 50$:

   • Frequency = 16
   • Class width = $50 - 40 = 10$
   • Frequency density = $\frac{16}{10} = 1.6$

Now you can draw the histogram:

• The first bar (0 < h ≤ 20) will have a height of 0.75.
• The second bar (20 < h ≤ 35) will have a height of 3.2.
• The third bar (35 < h ≤ 40) will have a height of 4.2.
• The fourth bar (40 < h ≤ 50) will have a height of 1.6.

The widths of the bars should correspond to the class widths (20, 15, 5, and 10 respectively).

Would you like more details or have any questions?

Here are 5 related questions:

1. How is frequency density useful in representing data in histograms?
2. How do histograms differ from bar charts?
3. Can you describe when to use histograms over other graphical representations?
4. Why do smaller class widths sometimes result in taller bars on a histogram?
5. How would the shape of the histogram change if the frequencies were all evenly distributed?

Tip: In a histogram, the area of each bar represents the frequency for that class, not the height directly.