Comprehensive Calculator Guide
This calculator gives the probability-weighted average of the outcomes and its standard deviation. A project losing 20,000 with 30%, gaining 10,000 with 50% or 50,000 with 20% has an expected value of 9,000 but an SD near 24,269.
Average and risk
Multiply each outcome by its probability and add. The SD measures risk; weights that don’t add to 1 are normalised.
How to Use
- Enter the outcomes, losses as negatives.
- Enter their probabilities or weights in the same order.
- Press “Calculate” to see the expected value and SD.
Formula Used
E(X) = Σ x·P(x) | Var = Σ P(x)(x − E(X))²
Practical Examples
- Example 1
- Project: 9,000, SD ≈ 24,269.
- Example 2
- Number cube 1–6: 3.5.
Important Tips
- Keep both lists aligned.
- Compare expected value and SD together.
- Estimate probabilities from data.
Common Mistakes to Avoid
- Expecting the average this time.
- Forgetting the minus on losses.
- Ignoring a small chance of a ruinous loss.
Frequently Asked Questions
- Must they add to 1?
- No, weights are normalised.
- Why the SD?
- It measures risk.
- Where is it used?
- Projects, investment, inventory.