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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
5
0.11
6
0.22
7
0.11
8
0.11
9
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




Calculate Expected Value

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



Understanding Expected Value


Formula and Calculation


Applications