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AAI JE (Technical) Official Paper 2020

Option 3 : 170, 120

ST 2: Strength of materials

2026

15 Questions
15 Marks
15 Mins

__Concept:__

(Mean Absolute deviation), MAD = \(\frac{{\mathop \sum \nolimits_{i = 1}^n \left| {\;{D_i} - {F_i}} \right|}}{n}\)

BIAS or Mean forecast error** **= \(\frac{{\mathop \sum \nolimits_{i = 1}^n \left( {{D_i} - {F_i}} \right)}}{n}\)

where,

D_{i} = Actual Demand, F_{i} = Predicted Demand, n = No of demands

**Calculation:**

**Given:**

D_{i} |
F_{i} |
D_{i} - F_{i} |
| D_{i} - F_{i} | |
---|---|---|---|

500 | 600 | -100 | 100 |

680 | 600 | 80 | 80 |

800 | 600 | 200 | 200 |

900 | 600 | 300 | 300 |

n = 4,

MAD = \(\frac {680}{4}\) = 170

Bias = \(480\over 4\) = 120

__Additional Information__

**Forecast error:**

**MAD = \(\frac{{\mathop \sum \nolimits_{i = 1}^n \left| {\;{D_i} - {F_i}} \right|}}{n}\)****Bias or Mean forecast error**= \(\frac{{\mathop \sum \nolimits_{i = 1}^n \left({{D_i} - {F_i}} \right)}}{n}\)- Mean square error = \(\frac{{\mathop \sum \nolimits_{i = 1}^n {{\left( {{D_i} - {F_i}} \right)}^2}}}{n}\)
- Mean Absolute percentage error, (MAPE) = \(\frac{{\mathop \sum \nolimits_{i = 1}^n |\;\frac{{{D_i} - {F_i}}}{{{D_i}}} \times 100\;|}}{n}\)
- Tracking Signal, TS = \(RSFE\over MAD\)
- RSFE = Running sum forecast error = \(\mathop \sum \limits_{i = 1}^n \left( {{D_i} - {F_i}} \right)\)
- Standard deviation, σ = √MSE , MSE = Mean square error