Expected Value Calculator - Raw Data

Expected Value Calculator - Raw Data Method

Enter your raw data values to calculate the expected value (mean). The calculator will automatically count frequencies, derive probabilities, and compute the expected value. This is useful when you have actual observations rather than known probabilities.

Enter Raw Data

Enter numbers separated by commas, spaces, or line breaks

Valid Data Points:9

Unique Values:5

Frequency Distribution

ValueCountProbability

540.4444

610.1111

720.2222

810.1111

910.1111

Total91.0000

Expected Value E(X)

6.3333

(Mean)

Variance Var(X)

2.0000

Standard Deviation σ

1.4142

Probability

E(X) = 6.33

0.44

0.11

0.22

0.11

Value

Understanding Raw Data Expected Value

What is This Method?

When you have raw observations (actual data points), the expected value is simply the arithmetic mean. The calculator counts how often each value appears, derives probabilities from frequencies, and computes E(X) = average of all values.

How It Works

Step 1: Count frequency of each unique value
Step 2: Calculate probability = count / total
Step 3: Compute E(X) = Σ(value × probability)
Result: Same as arithmetic mean

When to Use This Method

Surveys: Responses on a scale (1-5 ratings)
Experiments: Recorded measurements or counts
Sample data: Historical observations
Real-world data: Any dataset of numeric values

Example Applications

Test scores: Average performance in a class
Sales data: Expected daily sales based on history
Dice rolls: Experimental probability from trials
Survey responses: Average rating or response

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.