Math Problem Statement

James collects the running times of 50 athletes and records the data in the table below.

Time ( seconds) Frequency 3 8 30 6 3 Use interpolation to estimate the median. Give your answer correct to 1 decimal place.

You need to use the population variance formula, where you divide by .

Solution

To estimate the median using interpolation from the given frequency table, we first need to understand how the data is grouped and distributed. Here's how to proceed step-by-step:

Step

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Interpolation
Median Estimation
Population Variance

Formulas

Median (Interpolation Formula): L + [(n/2 - F)/f] * h
Population Variance Formula: σ² = Σ(x - μ)² / N

Theorems

None (This is based on statistical formulas)

Suitable Grade Level

Grades 10-12

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