Expected Value Calculator - Grouped Data

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.)
Response times: Average from time intervals

Understanding Expected Value

Formula and Calculation

Applications

Calculate Expected Value

Use the calculator below to compute the expected value with step-by-step solutions and detailed explanations.