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To solve the problem, we need to calculate the mean (rata-rata) and mode (modus) of the given data set. 

### Step 1: Calculate the Mean
The mean can be calculated using the formula:

\[
\text{Mean} = \frac{\sum (x \times f)}{\sum f}
\]

where:
- \( x \) = data values
- \( f \) = frequencies of the data values

Given dataTo solve the problem, we need to calculate the mean (rata-rata) and mode (modus) of the given data set. 

### Step 1: Calculate the Mean
The mean can be calculated using the formula:

\[
\text{Mean} = \frac{\sum (x \times f)}{\sum f}
\]

where:
- \( x \) = data values
- \( f \) = frequencies of the data values

Given 
- \( x = 3, 4, 5, 6 \)
- \( f = 10, 15, 12, 14 \)

Let's compute \(\sum (x \times f)\) and \(\sum f\).

\[
\sum (x \times f) = 3 \times 10 + 4 \times 15 + 5 \times 12 + 6 \times 14
\]
\[
= 30 + 60 + 60 + 84 = 234
\]

\[
\sum f = 10 + 15 + 12 + 14 = 51
\]

So, the mean is:

\[
\text{Mean} = \frac{234}{51} \approx 4.588
\]

### Step 2: Calculate the Mode
The mode is the data value with the highest frequency.

From the frequency table:
- Frequency of 3 = 10
- Frequency of 4 = 15
- Frequency of 5 = 12
- Frequency of 6 = 14

The highest frequency is 15, which corresponds to the data value of 4. Hence, the mode is 4.

### Final Answer
- Mean (rata-rata) ≈ 4.6 (rounded)
- Mode (modus) = 4

Thus, the correct option is:

**4.6 dan 4**

Would you like more details or have any further questions?

### Related Questions
1. How do you calculate the median from a frequency distribution?
2. What is the difference between mean, median, and mode?
3. How would you calculate the variance and standard deviation for this data set?
4. How do outliers affect the mean and mode of a data set?
5. Can a data set have more than one mode?

**Tip:** When rounding the mean, always consider the required decimal places based on the problem's context.

Dari suatu penelitian diperoleh data sebagai berikut: Data: 3, 4, 5, 6 Frekuensi: 10, 15, 12, 14 Maka rerata dan nilai modus berturut-turut adalah....

Learn how to calculate the mean and mode from a frequency distribution dataset: Data: 3, 4, 5, 6 with frequencies 10, 15, 12, and 14. This problem demonstrates key concepts in statistics, including the calculation of mean and identification of mode.

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