Overview
This lecture explains how to estimate the mean from grouped data using a frequency table, focusing on finding midpoints and performing calculations.
Steps for Estimating the Mean from a Grouped Frequency Table
- Grouped data tables list value intervals (e.g., 0–10, 10–30) and their frequencies.
- To estimate the mean, first add a column for the midpoint of each group.
- The midpoint is found by averaging the lower and upper boundaries of each group.
- Add another column for the product of frequency and midpoint for each group.
- Calculate all midpoint values for each group interval.
- Multiply each frequency by its group's midpoint to fill the frequency × midpoint column.
- Find the total frequency by summing all frequencies.
- Find the total for the frequency × midpoint column.
- Estimate the mean by dividing the total of frequency × midpoint by the total frequency.
- Round the final answer appropriately based on standard rounding rules.
Worked Example
- Example midpoints: (0–10 → 5), (10–30 → 20), (30–50 → 40), (50–60 → 55), (60–80 → 70), (80–100 → 90), (100–120 → 110)
- Example frequency × midpoint products: 7×5=35, 11×20=220, 14×40=560, 16×55=880, 20×70=1400, 9×90=810, 3×110=330
- Example total frequency: 80
- Example sum of frequency × midpoint: 4235
- Mean estimate: 4235 ÷ 80 = 52.9375, rounded to 52.94
Key Terms & Definitions
- Grouped Data — Data presented in intervals rather than individual values.
- Frequency — Number of data points within an interval.
- Midpoint — The average of the upper and lower boundaries of an interval.
- Estimated Mean — An approximation found by dividing the sum of (frequency × midpoint) by the total frequency.
Action Items / Next Steps
- Practice finding midpoints, frequency × midpoint, and estimating mean for other grouped frequency tables.
- Remember to show all working steps in your exam for partial credit.