Math Problem Statement

For the following set of data, find the percentage of data within 2 population standard deviations of the mean, to the nearest percent. Data Frequency 66 22 99 77 1010 1010 1111 1414 1515 1818 1616 1515 1818 99 1919 88 2020 11

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Standard Deviation
Mean
Normal Distribution

Formulas

Weighted mean formula: \(\mu = \frac{\sum (x \cdot f)}{\sum f}\)
Population standard deviation formula: \(\sigma = \sqrt{\frac{\sum f \cdot (x - \mu)^2}{\sum f}}\)
Percentage formula: \(\text{Percentage} = \frac{\text{Number of data values within 2}\sigma}{\text{Total number of data values}} \times 100\)

Theorems

Empirical Rule

Suitable Grade Level

Grades 10-12