Page 2: Advanced Applications and Problem Solving

This page focuses on a complex example involving employee ages and demonstrates how to find missing frequency values using the estimated mean.

Example: Employee Ages Problem

• Age ranges: 20-30, 30-35, 35-40, 40-50, 50-80 years
• Missing frequency value 'y' to be calculated
• Given estimated mean: 34.75 years

Highlight: Problem-Solving Process

• Use of midpoints: 25, 32.5, 37.5, 45, 65
• Total frequency: y + 102
• Solution: y = 9.75

Definition: When solving for missing frequencies, use the fact that the sum of (midpoint × frequency) divided by total frequency equals the estimated mean.

Vocabulary:

• Estimated mean: The approximate average calculated using class midpoints
• Frequency: The number of occurrences in each class interval

Page 1: Calculating Estimated Means from Frequency Tables

This page demonstrates the calculation of estimated means from frequency tables using two detailed examples involving fish lengths and student heights.

Example: Fish Length Calculation

• Table shows lengths of 100 fish
• Class intervals: 0-10, 10-20, 20-30, 30-40, 40-50 cm
• Frequencies: 21, 29, 17, 31, 12
• Final estimated mean: 25.9 cm

Definition: The estimated mean is calculated by multiplying each midpoint by its frequency, summing these products, and dividing by the total frequency.

Highlight: Student Height Example

• Heights of 50 students analyzed
• Class intervals: 110-120, 120-130, 130-140, 140-150, 150-160 cm
• Calculated mean: 139.6 cm

Vocabulary:

• Midpoint: The center value of a class interval
• Modal class interval: The interval containing the highest frequency
• Class interval: A range of values grouped together