To find the average height (mean) from the given frequency distribution, we follow these steps:

1. Find the midpoint for each height class.

The midpoint is calculated as:

$\text{Midpoint} = \frac{\text{Lower bound} + \text{Upper bound}}{2}$

The midpoints for each class are:

• $160 - 164$: $\frac{160 + 164}{2} = 162$
• $165 - 169$: $\frac{165 + 169}{2} = 167$
• $170 - 174$: $\frac{170 + 174}{2} = 172$
• $175 - 179$: $\frac{175 + 179}{2} = 177$
• $180 - 184$: $\frac{180 + 184}{2} = 182$

2. Multiply the midpoint by the frequency for each class.

The frequency is provided in the table:

$\text{Sum of } (\text{Midpoint} \times \text{Frequency}) = (162 \times 2) + (167 \times 7) + (172 \times 10) + (177 \times 8) + (182 \times 3)$

3. Sum of frequencies

Total frequency $= 2 + 7 + 10 + 8 + 3 = 30$.

Now, I will calculate the sum of the products and the average height.The average height of the group is 172.5 cm, which corresponds to option D.

Would you like more details or have any questions? Here are five related questions to expand your understanding:

1. How is the midpoint calculated in a frequency distribution table?
2. Why is it important to calculate the midpoint in grouped data?
3. How does the frequency influence the calculation of the mean?
4. What would happen if we had unequal class intervals?
5. How would you calculate the median or mode from this table?

Tip: Always check if the class intervals are consistent when calculating the midpoint to ensure accurate results.