Statistics

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 P_k

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:

where:

P is the percentile of interest
i is the percentile location
N is the number in the data set

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.
b. If i is not a whole number, the PTh percentile value is located at the whole number part of i+1

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
Step 2. Calculate the percentile location:
Step 3. Determine the location: Because i is not a whole number, step 3(b) is used. The value of i+1 is 2.4+1, or 3.4. The whole number part of 3.4 is 3. The 30th percentile is located as the third value. The third value is 2, so 2 is the 30th percentile.

Percentiles of grouped data.
The k-th percentile denoted by P_k is computed as follows:

where:

L is the lower limit of the class containing P_k
f is the frequency of the class containing P_k
h is the width of the class containing P_k
C is the cumulative frequency of the class preceding the class containing P_k

Here, the cumutative frequency just greater than is the class containing P_k (K=1,2,...,99)

Determine P₈₀ from the following distribution

Class	Frequency	Cumulative frequency
0-5	20	20
5-10	15	35
10-15	31	66
15-20	22	88
20-25	10	98
25-30	2	100

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