Math Problem Statement

Cari rata-rata (Find the average) based on a frequency distribution table

Solution

The table in your image seems to represent a frequency distribution, likely based on age intervals or scores. The request, "Cari rata-rata (x̄)" translates from Indonesian as "Find the average (mean) (x̄)".

To calculate the mean, we need the following information:

  1. Class intervals (or scores): Represented by the intervals such as 45-49, 50-54, etc.
  2. Frequencies (f): These are the values below "skor," which are the counts of occurrences for each interval.

Steps to calculate the mean:

  1. Midpoints (m): First, calculate the midpoint for each class interval by averaging the lower and upper boundaries. For example, for 45-49, the midpoint would be: m=45+492=47m = \frac{45 + 49}{2} = 47

  2. Multiply midpoints by frequencies: For each class interval, multiply the midpoint by the corresponding frequency (f).

  3. Sum of all midpoint-frequency products: Add up all the products from step 2.

  4. Sum of all frequencies: Add all the frequencies.

  5. Mean (x̄): The formula for the mean is: xˉ=Σ(fm)Σf\bar{x} = \frac{\Sigma (f \cdot m)}{\Sigma f}

Would you like me to calculate this for you using the values from the table?


5 Related Questions:

  1. How is a class midpoint calculated in a frequency distribution?
  2. What is the difference between a weighted average and a simple average?
  3. How do you find the median from a frequency table?
  4. What is the role of frequencies in calculating statistical measures like the mean?
  5. How do you determine the mode from a grouped frequency distribution?

Tip: When working with frequency distributions, using midpoints is key to simplifying calculations like the mean and variance.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Mean (Average) Calculation

Formulas

Class midpoint: m = (Lower Bound + Upper Bound) / 2
Mean: x̄ = Σ(f * m) / Σf

Theorems

Arithmetic Mean Theorem

Suitable Grade Level

Grades 9-12