In today's data-driven world, information is generated and found anywhere. It may come from the most common outlets of information like the internet and television, to the people around you using their phones. Business Intelligence is used to make sense of this data and gain valuable insights. In this article, I will be exploring some of the key topics which are often introduced to anyone learning statistics.

Contingency Table and Measures of Variation

Contingency Table

Imagine you're running a small e-commerce business and want to understand the relationship between customer age and the likelihood of purchasing a product. For these kinds of scenarios, a contingency table can help because it displays data in a matrix format. It's a fundamental tool in Business Intelligence that shows the frequency of observations for different combinations of variables.

In our example, the table rows could represent age groups while the columns could represent purchase decisions (yes/no). This makes it easy to see the proportion between certain age groups which buy your product and certain age groups which don’t, possibly hinting which group is more likely to buy your product.

Measures of Distribution and Variation

Once you've organized your data in a contingency table, it's time to understand its distribution and variation. Measures like mean (average), median (middle value), and mode (most frequent value) help you grasp the central tendency of your data. However, this isn’t necessarily all that helpful until you understand variation. Tools like standard deviation tell you how spread out your data is from the central tendency. This is important because it tells us how precise or clustered our data is.

Data Visualization

To make sense of your data quickly, visualization is key since numbers aren’t normally easily understandable. Some of the most common techniques used for visualizing distribution are histograms and area line graphs.

A histogram can show you the distribution of your data. However, buckets are usually made before a histogram to group your data especially when dealing with numerical distributions. Through the use of buckets, you can transform your data to be categorical in nature and it allows you to count the frequency of each bucket.

On the other hand, area line graphs are used to estimate the probability of a new value as these show a graph similar to a probability distribution function (PDF)

Understanding Normal Distribution, Kurtosis, and Asymmetrical Distributions

Normal Distribution

The normal distribution, often referred to as the bell curve, is a crucial concept in statistics. Many real-world phenomena, like product demand or employee performance, tend to follow this pattern because the population size often, much more so nowadays, reaches the minimum size of 100. Understanding normal distribution allows you to make predictions and set benchmarks. For instance, if you know your sales data follows a normal distribution, you can confidently predict that a certain percentage of your sales will fall within a specific range.

One of the important concepts when dealing with normal distributions is the 68-95-99.7 rule. Basically, it states that the proportion of your population is around 68%, 95%, and 99.7% when looking around the amounts of 1, 2, and 3 standard deviations respectively.

Kurtosis

Kurtosis measures the tailedness of a distribution. A high kurtosis means data has heavy tails and more extreme values. In contrast, a low kurtosis indicates data with light tails and fewer extreme values. An example of its application would be when you're analyzing investment returns. Understanding kurtosis helps you assess the risk associated with different investment options.

Asymmetrical Distributions

Not all data fits the normal distribution. Real-world data often exhibits asymmetry, meaning it's skewed to one side. For instance, income distribution is typically positively skewed because a few individuals earn exceptionally high incomes. Recognizing and understanding asymmetrical distributions is vital in fields such as finance and economics.

Sampling

In Business Intelligence, you often deal with extensive datasets. Sampling is the process of selecting a smaller subset of data for analysis so that you don’t need to study the entire population. Proper sampling techniques such as random, stratified, and cluster sampling ensure that your subset accurately represents the whole dataset, saving time and resources while providing reliable insights. While there are various techniques, it is important to think about the right sampling technique to use and even use a mix of these so that we can eliminate the most amount of noise or bias that we can when sampling.

Bivariate Data, Correlation, and Information Theory

Bivariate Data Analysis

Businesses often need to analyze how two variables are related. For instance, you might want to understand how advertising spending affects sales revenue. Bivariate data analysis explores the relationship between two variables, helping you make informed decisions. Scatter plots are a common visualization tool for bivariate data, not only allowing you to see the correlation of these, but also allowing you to see patterns and trends.

Correlation

Correlation quantifies the strength and direction of a linear relationship between two variables. A positive correlation means as one variable increases, the other tends to increase as well (e.g., advertising spending and sales revenue). A negative correlation means as one variable increases, the other tends to decrease (e.g., product price and sales volume). Correlation coefficients such as Pearson's r, provide a numerical measure of this relationship.

Information Theory and Entropy

In this age of information, managing and extracting valuable insights can be quite overwhelming even for people who have been working in the industry of big data for a long amount of time. Studying information theory helps measure the uncertainty or information content of data. By understanding it, you can prioritize data that carries the most information and ignore redundant or irrelevant data. This is invaluable in fields like cybersecurity, where identifying unusual patterns can flag potential threats.

Entropy is one of the important concept in information theory because it helps us understand the concept of randomness a lot better. In math, there are a lot of random things like variables or certain values. However, some of these are predictable even though these are random in nature such as the random numbers produced by random number generators. Entropy tells us the predictability of something no matter how random it is. If the entropy of something is large, it is not predictable and provides new information for us to work with.

Regression Analysis

When you want to go beyond correlation and make predictions, regression analysis comes into play. It helps you understand the relationship between a dependent variable (e.g., sales revenue) and one or more independent variables (e.g., advertising spending and product price). Regression models provide equations that can predict outcomes based on input variables, aiding in decision-making and future planning.

In conclusion, Business Intelligence contains indispensable tools for businesses striving to thrive in a data-driven world. They provide the means to organize, analyze, and gain insights from complex data, ultimately guiding decision-making and strategy development. Understanding these key concepts, from contingency tables to regression analysis, empowers professionals across various industries to harness the power of data effectively and make informed decisions that drive success.

Posted using Honouree