Math Problem Statement

Determine the mean and standard deviation for a grouped frequency distribution of daytime household temperature data using the provided class midpoints and frequencies.

Solution

The problem displayed involves determining the mean and standard deviation for a grouped frequency distribution of household temperature data. Here's how we can solve it step by step:

  1. Class Midpoint Calculation:

    • For each class, the midpoint is calculated by taking the average of the lower and upper limits of each class.

    Midpoints provided:

    • Class 6164: 63.0\text{Class } 61-64: \ 63.0
    • Class 6567: 66.0\text{Class } 65-67: \ 66.0
    • Class 6869: 69.0\text{Class } 68-69: \ 69.0
    • Class 70: 70.0\text{Class } 70: \ 70.0
    • Class 7172: 72.0\text{Class } 71-72: \ 72.0

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Math Problem Analysis

Mathematical Concepts

Statistics
Grouped Data
Mean
Standard Deviation

Formulas

Mean = (Σf * x) / N
Standard Deviation = sqrt((Σf * (x - Mean)^2) / N)

Theorems

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Suitable Grade Level

Grades 10-12