Exploiting the Central Limit Theorem for Data Engineers: Big Data Quality Assurance | by Alex Aman | March 2024

How many times have you had to redo difficult tasks multiple times because analysts always managed to find some anomaly or error in the data and cost you a fortune.

Although there is a way to store all those extra runs and test data using central limit theory.

Handling data sets that contain billions of rows is a challenging task that carries significant operational and financial burdens. The testing phase, which is key to guaranteeing data quality and integrity, often requires significant computing power and, as a result, incurs significant costs. However, the light of hope for achieving cost-effectiveness without compromising data quality shines through the application of a basic statistical principle: the central limit theorem (CLT). By adopting CLT, Big Data engineers can ensure the high quality of their datasets while significantly reducing the costs associated with computing resources, especially in cloud environments where these costs can quickly escalate.

Imagine a gigantic sphere where each sphere represents a piece of data. These are not just any balls; some are shiny and new (high-quality data), some are a little worn (usable but not perfect), and some are deflated (bad data). To check the overall quality of the “data”, you grab random handfuls of balls ( Samples). Your goal is not to examine every single ball in the box, but to get a good idea of ​​what the average ball looks like.

As you look at more and more handfuls, according to the Central Limit Theorem (CLT), the population mean of the sample starts to replicate and closely match the normal distribution of the entire spherical well. This remarkable pattern reveals that despite the randomness of each scoop, you can predict the overall quality of the data set – just as accurately as if you were evaluating each individual ball. This is CLT in action, suggesting that even a series of small, random samples can accurately reflect the quality of a larger data set.

Using CLT allows big data engineers to perform quality checks on smaller, randomly selected samples of data rather than the entire data set. This approach significantly reduces the computational load, which directly translates into lower cloud computing costs. Additionally, by facilitating faster iterations and enabling more frequent quality assessments, CLT increases the overall agility of the data quality assurance process.

Determining the optimal sample size involves balancing statistical significance with operational efficiency. While the 95% confidence level and 5% deviation serve as common benchmarks and have a total of 30+ samples, adjustments may be necessary based on specific data characteristics and quality requirements. For skewed distributions, larger sample sizes may be required to ensure representativeness.

It is essential that the sampled subsets accurately represent the entire data set. The use of random sampling techniques is essential to avoid bias, and in heterogeneous data sets, stratified sampling can ensure that all segments of the population are adequately represented.

The strength of CLT lies in its ability to generalize findings from sample tests to the entire data set. This ability to scale results from a subset to the entire population makes CLT an indispensable tool for big data engineers to effectively maintain data quality.

The Central Limit Theorem not only offers a statistically correct method for data quality assurance, but also represents a strategic approach to cloud computing cost management. By enabling the testing of smaller samples of data, CLT reduces the need for large-scale computing resources, providing the dual benefit of maintaining data integrity and increasing cost effectiveness. As big data continues to evolve, leveraging statistical principles like CLT will be key to tackling data quality assurance challenges in a cost-effective manner. CLT is a testament to the synergy between statistical theory and practical, cost-effective big data engineering practices.

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