Mean Estimation from Grouped Data

This interactive simulation demonstrates why we use the midpoint of each group when estimating the mean from grouped data.

Interactive Simulation

Number of data points: 250

Number of groups: 8

Data distribution:

Actual frequency bars

Theoretical frequency lines

Statistics

True Mean: -

Estimated Mean (Midpoints): -

Difference: -

Percentage Error: -

Why Midpoints?

When data is grouped, we don't know the exact values within each group. Using the midpoint assumes that data points are evenly distributed within each group.

This is a reasonable assumption because:

It minimises the average error
It works well for most distributions
It's simple to calculate

Try different distributions and group sizes to see how the accuracy changes!

Group Details

Mathematical Explanation

When we have grouped data, we estimate the mean using:

Estimated Mean = Σ(midpoint × frequency) / Σ(frequency)

Where:

midpoint = (lower bound + upper bound) / 2
frequency = number of data points in that group

This works because the midpoint represents the "average" position of all data points within that group, minimising the overall estimation error.