Math Problem Statement
Solution
To calculate the 85th percentile for the given dataset, we follow these steps:
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Arrange the data in ascending order (this step is unnecessary here, as the data is already sorted):
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Calculate the rank corresponding to the 85th percentile using the formula: Where:
- is the percentile (0.85 for the 85th percentile),
- is the number of data points.
In this case, , so the rank is:
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Interpret the rank: The rank 9.35 means that the 85th percentile lies between the 9th and 10th data points in the ordered list.
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Interpolate between the 9th and 10th data points:
- The 9th data point is ,
- The 10th data point is .
To interpolate, we use the formula:
So, the 85th percentile of the data is approximately 63.6.
Would you like more details on the interpolation method or percentile calculations?
Here are five questions to expand on this topic:
- How are percentiles different from quartiles?
- How does interpolation work in percentile calculations?
- What are some applications of percentiles in real-world data analysis?
- How would the method change if the data weren't already sorted?
- How does the choice of formula affect percentile calculation methods?
Tip: When calculating percentiles, always make sure the data is sorted in ascending order before applying the percentile formula.
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Math Problem Analysis
Mathematical Concepts
Percentiles
Statistics
Interpolation
Formulas
Percentile rank: Rank = P * (N + 1)
Interpolation formula: Percentile value = x_low + (x_high - x_low) * (Rank - floor(Rank))
Theorems
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Suitable Grade Level
Grades 10-12