# 10.1.3b Statistical Methods to Determine Mean and Dispersion and Definition of Variables

### Intended learning outcomes: Produce an overview on statistical methods to determine mean and dispersion. Identify definitions of variables, each calculated at the end of a statistical period.

Continuation in next subsection (10.1.3b).

Mathematical statistics offers various methods for determining the mean, deviation, expected value, and dispersion (scattering)[note 1003] of measured values for a time series. Its ability to reproduce the demand for a demand model accurately depends upon the situation. Figure 10.1.3.3 shows a morphology of possible statistical features and the statistical methods that they characterize.

Fig. 10.1.3.3      Statistical methods to determine mean and dispersion.

1. Calculation of dispersion. Two basic methods are used:
• Extrapolation, or estimation by calculation of deviations of individual values in the previous statistical periods from the mean, postulated by the demand model.
• Direct, that is, retrospective determination of the forecast error as the difference between actual demand and projected demand according to the demand model.
2. Measure of dispersion. There are two standards here:
• Mean square deviation σ: (sigma, i.e., standard deviation)
3. Weighting of values. Most commonly encountered are:
• Equal weighting of all measured value
• Exponential weighting of measured values in the direction of the past

In most cases, we only measure satisfied demand for all models. This equates consumption with demand. The basic problem with this measure­ment is that real demand is not taken into account. The customer order receipts mentioned in Figure 10.1.3.1 may have been higher, for example, if a better demand model had resulted in better availability. Strictly speaking, the customer orders that could not be filled should have been measured as well. The problem with this, however, is that the customer orders may be filled at a later time period. At that time, there may be other orders that will then be unfilled, etc. Determining the exact amount of demand in the past by employing a “what would have happened if” method rapidly proves itself redundant; later demand on the time axis is most likely dependent on satisfied demand in the preceding periods on the time axis.

The following sections use the variables defined in Figure 10.1.3.4. The nomenclature was chosen in such a way that the index always shows the point at the end of the statistical period in which a value is calculated. The period to which the value refers is shown in parentheses.

Fig. 10.1.3.4      Definitions of variables, each calculated at the end of a statistical period.

## Course section 10.1: Subsections and their intended learning outcomes

• ##### 10.1 Overview of Demand Planning and Forecasting Techniques

Intended learning outcomes: Produce an overview on the problem of demand planning. Present the subdivision of forecasting techniques. Disclose principles of forecasting techniques with extrapolation of time series and the definition of variables.

• ##### 10.1.1 The Problem of Demand Planning

Intended learning outcomes: Disclose the difference between human forecasting and IT-supported forecasting techniques with regard to a forecast’s precision. Present a possible demand planning procedure.

• ##### 10.1.2 Subdivision of Forecasting Techniques

Intended learning outcomes: Explain one possible breakdown of forecasting techniques. Disclose another possible subdivision of forecasting techniques.

• ##### 10.1.3 Principles of Forecasting Techniques with Extrapolation of Time Series

Intended learning outcomes: Present an example of a time series. Explain possible and common demand models.

• ##### 10.1.3b Statistical Methods to Determine Mean and Dispersion and Definition of Variables

Intended learning outcomes: Produce an overview on statistical methods to determine mean and dispersion. Identify definitions of variables, each calculated at the end of a statistical period.