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The question is asking to calculate the standard deviation \( s \) from a frequency distribution table with different interval classes. Here is the breakdown of the table provided:

| No urut | Kelas interval | Frekuensi (Frequency) |
|--------|-----------------|-----------------------|
| 1      | 10 – 19         | 2                     |
| 2      | 20 – 29         | 3                     |
| 3      | 30 – 39         | 5                     |
| 4      | 40 – 49         | 8                     |
| 5      | 50 – 59         | 10                    |
| 6      | 60 – 69         | 9                     |
| 7      | 70 – 79         | 7                     |
| 8      | 80 – 89         | 4                     |
| 9      | 90 – 99         | 2                     |
| **Jumlah**  |                 | **50**                   |

### Steps to calculate standard deviation (using frequency distribution):

1. **Find the midpoint ( \( x_i \) ) for each class**:  
   Midpoint \( x_i \) of a class interval can be found by taking the average of the lower and upper bounds of the class.
   \[
   x_i = \frac{\text{Lower Bound} + \text{Upper Bound}}{2}
   \]

2. **Multiply each midpoint \( x_i \) by the frequency \( f_i \)** to calculate \( f_i x_i \).

3. **Calculate the mean** \( \bar{x} \):
   \[
   \bar{x} = \frac{\sum (f_i x_i)}{\sum f_i}
   \]
   
4. **Find the squared deviations** \( (x_i - \bar{x})^2 \), and multiply them by the frequencies \( f_i \) to get \( f_i (x_i - \bar{x})^2 \).

5. **Sum up** all \( f_i (x_i - \bar{x})^2 \), and divide by \( \sum f_i - 1 \) to find the variance.

6. **Standard deviation** \( s \):
   \[
   s = \sqrt{\frac{\sum f_i (x_i - \bar{x})^2}{\sum f_i - 1}}
   \]

Let me calculate this step by step for you.The calculated mean \( \bar{x} \) is 56.1, and the standard deviation \( s \) is approximately 19.73.

Would you like more details on the calculations or any specific step?

Here are 5 related questions to explore further:
1. How would the standard deviation change if the frequencies were doubled?
2. What is the significance of the standard deviation in this context?
3. How would the calculation differ for a population standard deviation versus a sample standard deviation?
4. How can you calculate the variance from the standard deviation?
5. What other measures of spread (besides standard deviation) are commonly used in statistics?

**Tip**: In frequency distribution tables, the midpoint is crucial for representing the entire class interval with a single value.

Dalam tabel distribusi frekuensi seperti di bawah ini, hitung s dengan mempergunakan rumus-rumus simpangan yang berbeda-beda.

Learn how to calculate the standard deviation for a frequency distribution table with different class intervals, including the steps to find the midpoint, mean, and variance. The dataset includes class intervals and their respective frequencies. Suitable for high school students learning statistics.

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