# Unit 31-LO3 Apply statistical methods in business planning-BTEC-HND-Level 4 & 5

Course: Pearson BTEC Levels 4 and 5 Higher Nationals in Business

Predictive modeling is a method of statistical data modeling used in business planning. It’s based on the idea that if you can measure a large and enough data set, then from it extract features that are key to one or more outcomes (predictors), then you may be able to predict the occurrence of those outcomes with good accuracy.

The task at hand for predictive analysts is to find features that relate to an outcome and model their values such that they reproduce how well they correlate with the observed outcome for different subsets of its values, like predicting diabetes based on blood sugar levels.

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## Statistical methods for business planning:

### Applying statistical methods to a number of areas of business planning and operations management, including inventory management and capacity management.

It’s important for business planners to mathematically model the statistical properties of their organization and anticipated future changes. Operations management, which affects things like inventory and capacity planning, is a significant part of this.

The two most commonly used models that have been developed are Statistical Process Control (SPC) and Data Envelopment Analysis (DEA). SPC focuses on stability in particular areas with regard to potential processes or products while DEA evaluates different aspects of operations within a company by assigning “weights” to each aspect according to how it contributes towards its efficiency.

For instance, an analyst will assign 100 units as the maximum amount for human hours needed per day for this aspect in relation to others; 50 units as assigned by other analysts; 10 units as the average score of the industry performance, etc.

The main difference between these two techniques is that DEA allows for cross-sectional comparisons between companies; a feature that SPC lacks.

## Measures of variability:

### The issue of variability in business processes (e.g. arrival rates of customers and time taken to deal with customers), and how this leads to a trade-off between waiting time and process utilization.

Variability in business processes is often overlooked and regarded as “OK”.

Variability in the arrival rates of customers, for example , can lead to poor performance by staff who typically spend too much time being idle waiting for a customer to arrive when there are many customers arriving simultaneously.

Variable work content, to provide another example, can lead to poor productivity because it forces employees to occasionally switch between tasks that they are known for being good at but may not be well suited for.

A trade-off between waiting time and process utilization is one aspect of the queuing models for service systems with a queue.

In general, a business will try to increase its rate of productivity by investing in additional equipment and employees, but that investment can lead to an increased level of system complication – which could both result in higher costs and lower efficiency as customers wait for assistance.

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### Statistical process control in quality management

Statistical process control (SPC) is an approach to quality management that uses statistically-based research techniques for analyzing data on a part, product, or process variation. Typically this data is analyzed and compared against a norm for the end result of a production line in order to figure out if changes are needed.

Some examples of items this would be used on include: A manufacturing line- Item- Customer Issues- Product Quality Assurance.

Some advantages of SPC include better understanding the statistical distributions in products and processes as well as the ability to readily understand what impacts the outputs have on things like customer satisfaction.

## Measures of probability:

### Probability distributions and application to business operations and processes

The term probability distribution refers to the distribution of probabilities over some collection of events within a population. The most popular instance of this type is a so-called “normal distribution,” whose probabilities are given by the formula P(x) = 1/(x+1)⁻¹ with x being an event or observation at random and uniformly distributed in the interval from 0 to 1 (so, for example, if we picked one person out of 10000, then their odds would be 10001/101000 or 10⁻¹).

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Despite all those weird constants that need multiplying and dividing by square roots before getting back to the right answer every time you want to find their chance out of 1000 flips, it’s still a remarkable achievement that we can so easily state, “given 1000 trials and one event X, then the odds of observing it are 100″.

An application in business operations and processes is to create a Feedback Loop by rewarding members for responding with insightful solutions.

A feedback loop is a process of giving back information, which enables you to react to the information or have it modified in some way. It can be applied at any stage of the process, ensuring that the quality remains high and improving outcomes.

### A normal distribution (e.g. weights and measures regulations and statistical process control)

A normal distribution is an ideal high-quality, large-scale fabrication process for products. Statistical Process Control (SPC) is an engineering approach to identify and control variability in a system or process of events that can cause defects. This technique requires the central limit theorem which states that any uniform or random error will be normally distributed. If you’d like to learn more about this concept, then please visit General Electric’s article.

### Poisson distribution (e.g. customer arrival rates) and binomial distribution (e.g. inspection sampling)

A Poisson distribution is a discrete probability distribution that describes the number of events, whose rate of occurrence in a given time interval is constant and equal to its mean quantity per unit interval. It can be applied if one is looking for the number of events that will happen each second or minute but does not care about when they’ll happen.

It’s most commonly used for modeling certain types of naturally occurring phenomena where some kind of quantity (such as the number of mouse traps) tends to self-equilibrate in space as well as through time, such as randomly dropping balls or molecules diffusing into the air from a fixed point.

### Inference (e.g. margins of error and confidence limits).

The inference is a statistic that examines the probability of an event. It’s often used to understand true outcomes when they cannot be measured directly.

There are two types of inference: statistical and inductive.

Statistical inference refers to calculations that can only be made if there is enough data for both sides in comparison, like calculating the mean or the standard deviation from a set of numbers, or comparing results for groups (states) based on how many people voted in the 2016 presidential election by racial groupings (white/Hispanic/other).

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Inductive inference relies on experiments where at least one variable isn’t controlled but tries to make conclusions about it anyway; for example, trying to determine what is causing higher crime rates by looking at which cities/states have higher murder rates and seeing if a common factor exists. Research is one way to draw conclusions about something, but it isn’t the only way.

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