Math Problem Statement

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....

Solution

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:

Mean=∑(x⋅f)∑f\text{Mean} = \frac{\sum (x \cdot f)}{\sum f}

Where:

  • xx is the data value
  • ff is the frequency
= 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!

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Mode

Formulas

Mean = (Σ (x * f)) / (Σ f)
Mode is the data point with the highest frequency

Theorems

Basic Statistical Measures

Suitable Grade Level

Grades 7-9

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