What percentile indicates the value where half the data set is above and half is below?

The 50th percentile, often referred to as the median, is the point in a data set where half of the values fall below it, and half are above it. This measure divides the data into two equal parts and is a crucial concept in statistics as it offers a clear indication of the central tendency of the distribution.

In contrast, the other percentiles—25th, 75th, and 90th—represent different positions within the data set where specific proportions of values lie below that threshold. The 25th percentile indicates that 25% of the data falls below this point, the 75th percentile shows that 75% of the data is below it, and the 90th percentile indicates that 90% of values are below this level. None of these measures bisect the data set into equal halves, which is specifically what the 50th percentile or median accomplishes. This characteristic makes the median particularly valuable in understanding the distribution of data, especially in skewed distributions where mean values may not provide an accurate representation.