The weights of 30 learners are: 22, 14, 18, 26, 32, 11, 29, 21, 15, 27, 34, 13, 24, 19, 20, 25, 25, 21, 10, 16, 28, 20, 17, 24, 12, 19, 22, 25, 33, 21. Construct a frequency distribution table using c

Step 1: List the given data in ascending order.
The weights of the 30 learners are:
22, 14, 18, 26, 32, 11
29, 21, 15, 27, 34, 13
24, 19, 20, 25, 25, 21
10, 16, 28, 20, 17, 24
12, 19, 22, 25, 33, 21

Sorted data:
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 24, 24, 25, 25, 25, 26, 27, 28, 29, 32, 33, 34

i) Construct a frequency distribution table.
Using class intervals of 10-14, 15-19, 20-24, etc., we calculate the frequency (f), midpoint (x), product of frequency and midpoint (fx), and cumulative frequency (cf) for each class.

Class Interval	Frequency (f)	Midpoint (x)	fx	Cumulative Frequency (cf)
10-14	5	12	60	5
15-19	6	17	102	11
20-24	9	22	198	20
25-29	7	27	189	27
30-34	3	32	96	30
Total	$\sum f = 30$		$\sum fx = 645$

ii) Identify the modal class.
The modal class is the class interval with the highest frequency. From the table, the highest frequency is 9, which corresponds to the class interval 20-24.
The modal class is $\boxed{\text{20-24}}$.

iii) Calculate the mean weight of the learners.
The mean ($\bar{x}$) for grouped data is calculated using the formula:

$$\bar{x} = \frac{\sum fx}{\sum f}$$

From the frequency distribution table:
$\sum fx = 645$
$\sum f = 30$

Substitute these values into the formula:

$$\bar{x} = \frac{645}{30}$$ $$\bar{x} = 21.5$$

The mean weight of the learners is $\boxed{21.5}$.

iv) Determine the median class.
The median class is the class interval where the median value lies.
The total number of learners ($N$) is 30.
The position of the median is $\frac{N}{2} = \frac{30}{2} = 15^{th}$ value.
Looking at the cumulative frequency column:

• The 5th value is in the 10-14 class.
• The 11th value is in the 15-19 class.
• The 20th value is in the 20-24 class. Since the 15th value falls between the 11th and 20th values, it is located in the 20-24 class. The median class is $\boxed{\text{20-24}}$.