https://file.aiquickdraw.com/mathbot/file/1727178418492t9mrke65.jpg

The table in the image shows the data and their respective frequencies:

- Data: 3, 4, 5, 6
- Frekuensi (Frequency): 10, 15, 12, 14

We are asked to find the mean (rata-rata) and mode (modus).

### 1. Mean (Rata-rata)
The formula for the mean is:

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

Where:
- \( x \) is the data value
- \( f \) is the frequency

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

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

Now, calculate the mean:

\[
\text{Mean} = \frac{234}{51} \approx 4.59 \ (\text{rounded to } 4.6)
\]

### 2. Mode (Modus)
The mode is the data value with the highest frequency. From the table, the frequency for 4 is the highest (15), so the mode is 4.

### Conclusion:
The mean is approximately 4.6, and the mode is 4. Therefore, the correct answer is:

**4.6 and 4**

Would you like further details or explanations?

### Related Questions:
1. How do you calculate median in this kind of data set?
2. What if two modes appear? How is bimodal data interpreted?
3. What is the relationship between mean, median, and mode?
4. How does skewness affect the mean and mode?
5. Can the mean of a data set ever be smaller than all the data values?

### Tip:
Always double-check your calculations for sums and products when working with data sets, especially when frequencies are involved!

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 frequency data. In this example, data values are 3, 4, 5, and 6 with corresponding frequencies of 10, 15, 12, and 14. Detailed steps to find the mean and mode for this dataset are provided, including the key formula for calculating the mean.

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