Refer to the given table below to answer Questions 9 - 11.

The value 'a' represents the "Less than cumulative frequency" for the class $130 \le h < 140$. This is the sum of the frequencies of the current class and all preceding classes.

$$a = \text{Frequency}(120 \le h < 130) + \text{Frequency}(130 \le h < 140)$$ $$a = 8 + 12 = 20$$

9. What must be the value of a in the table?
Answer: $\boxed{\text{20}}$

The value 'b' represents the "Greater than cumulative frequency" for the class $140 \le h < 150$. This is the sum of the frequencies of the current class and all succeeding classes.

$$b = \text{Frequency}(140 \le h < 150) + \text{Frequency}(150 \le h < 160) + \text{Frequency}(160 \le h < 170)$$ $$b = 14 + 7 + 9 = 30$$

Alternatively, the "Greater than cumulative frequency" for $130 \le h < 140$ is 42. Subtracting the frequency of this class (12) gives 'b'.

$$b = 42 - 12 = 30$$

10. What must be the value b in the table?
Answer: $\boxed{\text{30}}$

This value is directly given in the "Less than cumulative frequency" column for the class $150 \le h < 160$.
From the table, the "Less than cumulative frequency" for $150 \le h < 160$ is 41.
11. How many students stand less than 160 cm?
Answer: $\boxed{\text{41}}$

For Question 12:
We need to complete the table by calculating the Midpoint and Relative frequency (%) for each class interval, rounding to the nearest hundredths.

First, sum all the frequencies to find the total number of data points.

$$\text{Total Frequency} = 8 + 14 + 13 = 35$$

The midpoint is calculated as $\frac{\text{Lower Limit} + \text{Upper Limit}}{2}$.

• For 20-24: $\frac{20 + 24}{2} = \frac{44}{2} = 22$ (Matches given)
• For 25-29: $\frac{25 + 29}{2} = \frac{54}{2} = 27$
• For 30-34: $\frac{30 + 34}{2} = \frac{64}{2} = 32$

Relative frequency (%) is calculated as $\frac{\text{Frequency}}{\text{Total Frequency}} \times 100\%$.

• For 20-24: $\frac{8}{35} \times 100\% \approx 22.857\% \approx 22.86\%$ (Matches given)
• For 25-29: $\frac{14}{35} \times 100\% = \frac{2}{5} \times 100\% = 0.4 \times 100\% = 40.00\%$
• For 30-34: $\frac{13}{35} \times 100\% \approx 37.142\% \approx 37.14\%$

12. Complete the table below: (Round off decimal answers to the nearest hundredths)
Answer:

Class Interval	Frequency	Midpoint	Relative frequency (%)
20-24	8	22	22.86
25-29	14	$\boxed{\text{27}}$	$\boxed{\text{40.00}}$
30-34	13	$\boxed{\text{32}}$	$\boxed{\text{37.14}}$