Question

A TV seller predicts the demand at the rate of 600 units per month for the next four months. Actual demand is found 500, 680, 800 and 900 units, respectively. The mean absolute deviation (MAD) and the BIAS are ________ and ________, respectively.
1. 170, -120
2. -170, 120
3. 170, 120
4. 120, 170

Answer 1

Correct Answer - Option 3 : 170, 120

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:

Di	Fi	Di - Fi	| Di - Fi |
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

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