centils

Centils are a type of statistical measure used to divide a dataset into 100 equal parts. Unlike percentiles, which divide data into 100 parts, centils go a step further by identifying the specific points where these divisions occur. The first centil represents the value below which 1% of the data falls, the second centil marks the value below which 2% of the data falls, and so on, up to the 99th centil, below which 99% of the data lies. The 100th centil is equivalent to the maximum value in the dataset. Centils are useful for understanding the distribution of data and identifying extreme values. For example, in a large dataset of test scores, the 90th centil would indicate the score below which 90% of students scored. This helps in understanding relative performance. Calculating centils involves ordering the data and then determining the appropriate position for each centil. The formula for the position of the k-th centil is (k * (n + 1)) / 100, where n is the number of data points. If this position is not a whole number, interpolation between the adjacent values is often used. Centils provide a more granular view of data distribution compared to percentiles, allowing for finer distinctions within the dataset.