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Calculate the mean implied by the distribution
The expected return is 0.30×(−2%) + 0.50×8% + 0.20×14% = 6.2%. A separately stated value of 6% does not become the mean of this distribution merely because it is described that way.
Compute deviations from 6.2%
Using percentage-number returns, the deviations are −8.2, 1.8 and 7.8. Square them and apply the supplied probabilities.
| Return | Probability | Squared deviation from 6.2 | Weighted contribution |
|---|---|---|---|
| −2% | 30% | 67.24 | 20.172 |
| 8% | 50% | 3.24 | 1.620 |
| 14% | 20% | 60.84 | 12.168 |
| Total | 100% | 33.960 |
Explain the calculation around a 6% target
Using 6% as the reference instead gives a probability-weighted squared deviation of 34. This is a valid mean squared deviation from that specified target, but it is not the model variance. The difference is the squared gap between mean and target: (6.2 − 6)² = 0.04. Thus 33.96 + 0.04 = 34.
Take the square root in matching units
The square root of the actual variance is approximately 5.8275%. Dividing the weighted variance by three would add an inappropriate extra divisor. Dividing an unweighted sum by three would instead describe an equal-weight model.