Math Problem Statement
Solution
The problem provided is asking to calculate the mean (average) of grouped data using the class-mark method ("tanda-kelas" in Indonesian).
The table includes:
- Class intervals (Kelas interval): These are the ranges of values.
- Frequency (f): This represents the number of occurrences for each class interval.
Step-by-Step Solution
-
Calculate Class Mark (tanda-kelas): The class mark for each interval is the midpoint, calculated as:
-
Multiply Frequency (f) by Class Mark: Multiply the frequency of each interval by the corresponding class mark.
-
Calculate Mean: The formula for the mean is:
where:
- is the frequency.
- is the class mark.
- is the total frequency.
Calculations:
No urut | Kelas interval | Class Mark | ||
---|---|---|---|---|
1 | 20 - 24 | 2 | ||
2 | 25 - 29 | 5 | ||
3 | 30 - 34 | 13 | ||
4 | 35 - 39 | 17 | ||
5 | 40 - 44 | 17 | ||
6 | 45 - 49 | 6 |
Mean Calculation:
So, the mean of the grouped data is 37.
Would you like further details or clarification?
Here are 5 related questions you could explore:
- What is the importance of using class marks in grouped data?
- How would the mean change if the class intervals were different but the frequencies stayed the same?
- How can we calculate the mode and median for this grouped data?
- What is the difference between grouped and ungrouped data in statistics?
- How does the class width affect the accuracy of the calculated mean?
Tip: Always double-check your class marks and frequency products to avoid simple calculation errors when dealing with grouped data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Grouped Data
Class Mark
Formulas
Class mark (tanda-kelas) = (Lower limit + Upper limit) / 2
Mean (average) = Σ(f × x) / Σf
Theorems
-
Suitable Grade Level
Grades 10-12
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