## Probability & Statistics

This article explores the importance and use of probability and statistics within a business. Companies often have to cope with a degree of uncertainty and risk in their decision making. The collection and analysis of data is a key factor in easing ambiguous circumstances. Data is effectively analyzed using probabilistic and statistical models to evaluate past performance, understand the wants and needs of consumers, and draw important conclusions and relationships from the data. It is crucial for a business to understand the differences between statistical tools and to know which statistics will suit their needs best. The use of probability and statistics are useful tools in business forecasting as well.

Keywords Business Statistics; Correlation; Economic Forecasting; Expectation; Forecasting; Median; Mode; Outlier; Probabilistic Model; Probability; Qualitative Data; Quality Control; Quantitative Data; Regression; Risk; Statistical Model; Statistical Sampling; Statistics; Variance

### Statistics: Probability

### Overview

### Probability

Probability and statistics are essential concepts that arise in everyday situations, as well as in the business world. Business statistics is primarily concerned with drawing inferences about a particular population. The use of statistics and probability within the realm of business allows companies to make decisions while working in unpredictable circumstances. Statistics allow businesses to analyze various components of their company. Customer satisfaction, expectations, quality, and comparisons are all crucial aspects that need to be examined within a business. The application of statistics to business is what makes the exploration of these four areas possible.

### Probability

The concept of probability has been in use since the 16th century, and later branched out into its own mathematical field in the 17th century. Probability was often studied in gambling and other such games of chance that featured an aspect of ambiguity. Probability is currently used in a wide array of fields, including financial sectors such as insurance and investments, as well as in technological and medical industries.

### Statistics

The idea of statistical data arose in the 17th century through studies and collections of data involving population and the human life cycle. The formulation of the field of statistics was driven by probability and games associated with chance or risk, as well as to numerically quantify and describe populations. Currently, the area of statistics is concerned primarily with making inferences and drawing conclusions based upon a set of data. The study of statistics has infiltrated various other fields such as economics, business, finance, and medicine.

### Risk

The use of probability and statistics is associated with the concept of risk, an abstract measurement of unpredictability in a result. It supplies a ratio of how much an outcome will vary from what is expected during a given time interval. The concept of risk is often seen in financial sectors. The use and assessment of risk is frequently used by particular professions. One prime example is that of an actuary. Actuaries can work in a multitude of places but are commonly employed by insurance companies and consulting firms. Actuaries, as well as other risk managers, analyze risk on a daily basis using several statistical measurements.

Risk often presents itself in a business under numerous circumstances. According to Kallman (2005), the three main components in measuring risk are expectation, variance and time. The expected outcome, or mean, enables risk managers to use previous outcomes as a model for future results. The mean is calculated by dividing the summation of all outcomes by the total number of possible outcomes. Expectation can be a core part of decision-making in business. Companies can calculate expected profits and adjust their inventory accordingly in order to optimize their potential profit. Another useful measurement is variance, which is used to calculate a range for the possible values of an outcome. The square root of the variance results in a value known as the standard deviation. The length of time during which it is probable that a possible loss of capital can occur is also an important factor in measuring risk.

There can often be a degree of uncertainty or risk present within a business. The future is of primary concern for companies and it is also an entire realm of ambiguity. Businesses cannot change past performance, but they can attempt to predict future economic conditions and prepare their companies accordingly. Such strategies are known as economic forecasting. Forecasting often involves the analysis and thorough examination of specific statistics.

### Important Business Statistics

Consumer Price Index (CPI) is a key measurement of the economy's current condition, a representation of the cost of living and how this cost changes over time. This statistic can assist businesses in better understanding their customers by predicting which products and what quantity of products they will consume. It is a good indicator of inflation within an economy. The Producer Price Index and prices paid by farmers are also used as economic indicators (*Economic Indicators*, 2013).

When a company provides a service, Key Performance Indicators (KPIs), are critical statistics that allow the business to evaluate its performance and identify any potential problem areas. The most important KPI is billable hour efficiency. This statistic enables a company to measure its profit by looking at the amount of hours sold, which directly contributes to the inflow of cash within a business.

It is essential that businesses and their employees have a good understanding and firm grasp of the use of probability and statistics. A critical aspect of running a successful business is consumer satisfaction and optimal performance. In order to achieve these goals, probability and statistics can aid decision makers in times of uncertainty by choosing a path in their best interest. It is important to be able to distinguish between various statistics and be able to select a method that will give a valuable result.

### Application

### Data Collection

The collection and analysis of data is a vital factor in probability and statistics. There are numerous ways to collect and categorize data. As mentioned, data from government indexes is a longstanding source. New techniques have emerged as well. Premise, for example, is “a US start-up that is challenging traditional economic data models by generating real-time information. The … company does this by gleaning price data from global ecommerce sites and by crowdsourcing data from people using Android phones in retail locations around the world. It can then provide real-time updates on price and inflation changes, allowing corporations and governments to react more quickly” (Bacon, 2013).

Data can be divided into two distinct parts, qualitative and quantitative. Qualitative data have no numerical value associated with them and can be broken down into descriptive categories. Quantitative data can be represented numerically and relationships can be drawn between the data and other values or measures. These types of data are collected by either counting or measuring, and are referred to as discrete data or continuous data, respectively. Tables, charts, and graphs are all used to display and study data. Histograms, box plots, stem-and-leaf plots, scatter plot, distributions and other representations are widely used.

- Histograms are common bar graphs used to display frequency distributions, or the rate at which a particular factor occurs. The height of each bar corresponds to the number of times an outcome is observed for a variable.
- Box plots graphically display percentiles. The first, second, and third quartiles, or the 25th, 50th, and 75th percentiles respectively, are represented in the plot. A line through the box representing the second quartile corresponds to the median of the data. Box plots are useful in identifying outliers.
- Stem-and-leaf...

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