Math Problem Statement
Solution
To estimate the mean height from a frequency polygon, we need to follow these steps:
Steps to calculate the mean:
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Determine class midpoints: From the x-axis, we can observe that the intervals are of equal width (about 25 cm). The midpoints are typically the middle of each interval on the x-axis.
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Estimate frequencies: From the y-axis, we can estimate the frequency (height of each point in the frequency polygon) at each interval.
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Calculate the total frequency: Sum the frequencies from all intervals.
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Calculate the weighted mean: Multiply each midpoint by its respective frequency, sum the results, and divide by the total frequency.
Let me estimate the midpoints and frequencies based on the graph:
Midpoints and Frequencies:
- Interval 1: 112.5 cm (midpoint), frequency ≈ 6
- Interval 2: 137.5 cm (midpoint), frequency ≈ 10
- Interval 3: 162.5 cm (midpoint), frequency ≈ 17
- Interval 4: 187.5 cm (midpoint), frequency ≈ 15
- Interval 5: 212.5 cm (midpoint), frequency ≈ 7
Next steps:
- I'll now calculate the estimated mean based on these midpoints and frequencies.The estimated mean height of the members of the football club is approximately 165.7 cm, rounded to one decimal place.
Would you like more details or have any other questions?
Here are five related questions you might want to explore:
- What is the significance of using midpoints in estimating the mean?
- How could this frequency polygon be used to estimate the median height?
- How does rounding the mean to one decimal place affect the accuracy of the estimate?
- Can frequency polygons be used for data comparison between groups?
- What would be the impact of extreme values (outliers) on the mean in a real dataset?
Tip: Always ensure that class intervals are clear and evenly spaced when calculating statistical estimates from grouped data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean Estimation
Grouped Data
Formulas
Mean = Σ(frequency × midpoint) / total frequency
Theorems
Weighted Mean Theorem
Suitable Grade Level
Grades 8-10
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