Math Problem Statement
Solution
To find an approximation for the sample mean from the given grouped data, we use the formula for the mean of a frequency distribution:
Where:
- is the frequency for each class.
- is the midpoint of each class (calculated as the average of the class interval).
Step-by-step calculation:
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Class intervals and frequencies (already provided):
- 0–4, 5–9, 10–14, 15–19, 20–24, 25–29, 30+
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Calculate the midpoints for each class:
- Midpoint of 0–4:
- Midpoint of 5–9:
- Midpoint of 10–14:
- Midpoint of 15–19:
- Midpoint of 20–24:
- Midpoint of 25–29:
- Midpoint of 30+: Since the class is open-ended, we approximate the midpoint as 32.
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Multiply the frequency by the midpoint for each class.
Let me calculate the total for you.The approximate sample mean is .
Do you have any further questions or would you like additional details?
Here are 5 related questions you might want to explore:
- How do you calculate the median from grouped data?
- What is the difference between a sample mean and a population mean?
- How does changing class intervals affect the approximation of the mean?
- How can we calculate the variance and standard deviation for grouped data?
- What is the significance of using midpoints in frequency distribution?
Tip: In grouped data, the sample mean gives an estimate of the center of the data distribution, especially useful when the actual data values are not available.
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Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Sample Mean Calculation
Formulas
Mean (x̄) = Σ(f * x_m) / Σf
Theorems
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Suitable Grade Level
Grades 9-12
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