To find the mean (nilai rata-rata) of the grouped data in the table, we follow these steps:

1. Identify midpoints (xi) for each class interval by averaging the lower and upper bounds.
2. Multiply midpoints by frequencies (fi * xi) for each class.
3. Sum the products (Σ(fi * xi)).
4. Sum the frequencies (Σfi).
5. Calculate the mean using the formula:

$\text{Mean} = \frac{\Sigma(fi * xi)}{\Sigma fi}$

Let's apply this process:

Step 1: Midpoints (xi)

• For 10-14: $\frac{10 + 14}{2} = 12$
• For 15-19: $\frac{15 + 19}{2} = 17$
• For 20-24: $\frac{20 + 24}{2} = 22$
• For 25-29: $\frac{25 + 29}{2} = 27$
• For 30-34: $\frac{30 + 34}{2} = 32$
• For 35-39: $\frac{35 + 39}{2} = 37$

Step 2: Multiply midpoints by frequencies (fi * xi)

• For 10-14: $12 \times 4 = 48$
• For 15-19: $17 \times 8 = 136$
• For 20-24: $22 \times 5 = 110$
• For 25-29: $27 \times 6 = 162$
• For 30-34: $32 \times 4 = 128$
• For 35-39: $37 \times 3 = 111$

Step 3: Sum the products (Σ(fi * xi))

$48 + 136 + 110 + 162 + 128 + 111 = 695$

Step 4: Sum the frequencies (Σfi)

$4 + 8 + 5 + 6 + 4 + 3 = 30$

Step 5: Calculate the mean

$\text{Mean} = \frac{695}{30} \approx 23.2$

Thus, the mean value of the data is 23.2.

The correct answer is e. 23.2.

Would you like any more details or have additional questions?

Here are 5 questions to further explore this topic:

1. How would the result change if one of the frequencies doubled?
2. Can you explain why we calculate midpoints for grouped data?
3. What other measures of central tendency can be used in grouped data?
4. How can the median be calculated from the given frequency distribution?
5. What happens to the mean if all data values increase by a constant amount?

Tip: For grouped data, midpoints give a good estimate of the actual values within each interval, which helps in calculating the mean more efficiently.