How to Calculate Quartiles, Deciles, and Percentiles

The Organic Chemistry Tutor

This comprehensive math tutorial provides a deep dive into statistical measures of position: quartiles, deciles, and percentiles. It begins by defining each term and visualizing their relationships on a number line, establishing a clear conceptual foundation before moving into calculations. The video demonstrates how to calculate these values for both odd and even datasets using two distinct methods: finding the median physically by eliminating outer numbers, and using the position formula $L = \frac{k}{100}(n+1)$. A significant portion of the video focuses on the nuances of calculation, specifically how to handle results when the position formula yields a decimal. It explains the process of averaging the two surrounding data points to find the precise value. Furthermore, the video introduces a formula for finding the percentile rank of a specific data point, which is useful for standardized testing contexts. Finally, it guides viewers through constructing a cumulative relative frequency table and using it to determine deciles efficiently. This resource is highly valuable for algebra and statistics classrooms. It addresses common points of confusion, such as the difference between a percentile's "position" and its "value," and how to handle data that falls between two values. Teachers can use this video to introduce new concepts, reinforce calculation methods, or provide a refresher on reading cumulative frequency tables. The step-by-step examples with varying dataset sizes make it an excellent reference for students mastering data analysis.