Percentiles (or centiles).
Percentiles are measures that divide a group of data into 100 parts.
Percentiles are values that split your data into percentages in the same way that quartiles split data into quartes. Each percentile is referred to by the percentage with which it splits the data. so 10th percentile i sthe value that is 10% os the way through the data.
In general, the kth percentile is the value that is k% of the way through the data. It's usually denoted by Pk
Steps in determining the location of a percentile.
Step 1. Organize the numbers into an ascending order.
Step 2. Calculate the percentile location (i) by:
Step 3. Determine the location by either (a) or (b)
a. If i is a whole number, the Pth percentile is the average of the value at the ith location and the value at the (i+1)st location.
Determine the 30th percentile of the following eight numbers 1 2 4 3 5 3 5 2 6
Step 1. Organize the data into an ascending-order array: 1 2 2 3 3 4 5 5 6
Percentiles of grouped data.
The k-th percentile denoted by Pk is computed as follows:
Here, the cumutative frequency just greater than is the class containing Pk (K=1,2,...,99)
Determine P80 from the following distribution
Here . The cumulative frequency just greater than 80 is 88, so the class 15-20 contains P80
L=15, f=22, h=5, C=66, Therefore