Expected Value Calculator - Grouped/Frequency Data Method
Calculate expected value from grouped or binned data. Enter ranges (intervals) with their frequencies. The calculator uses the midpoint of each range as the representative value and computes the weighted average. This method is ideal for histogram data, survey responses with brackets, or any pre-grouped statistics.
Enter Ranges and Frequencies
Range StartRange EndFrequencyMidpoint
15.00
25.00
35.00
Total Frequency:25
Valid Groups:3
Group Summary
RangeMidpointFrequencyProbability
10 - 2015.0050.2000
20 - 3025.00120.4800
30 - 4035.0080.3200
Total251.0000
Expected Value E(X)
26.2000
(Weighted Mean)
Variance Var(X)
50.5600
Standard Deviation σ
7.1106
Probability
E(X) = 26.20
0.20
15.0
0.48
25.0
0.32
35.0
Midpoint Value
Understanding Grouped Data Expected Value
What is This Method?
When data is organized into ranges or bins (like a histogram), we use the midpoint of each range as the representative value. The expected value is the weighted average of these midpoints, weighted by the frequency (or probability) of each range.
How It Works
Step 1: Calculate midpoint = (min + max) / 2
Step 2: Calculate probability = frequency / total
Step 3: Compute E(X) = Σ(midpoint × probability)
Result: Weighted average of midpoints
When to Use This Method
Histogram data: Pre-binned frequency distributions
Survey brackets: Age ranges, income ranges, etc.
Grouped statistics: Published data in ranges
Census data: Population by age/income brackets
Example Applications
Age analysis: Average age from age brackets
Income studies: Expected income from salary ranges
Test scores: Average from grade ranges (0-50, 50-70, etc.)