Percentile: We show two methods for calculating a percentile: Method A: To find a pth percentileof a sample of rz observations:

1. Order the n observations from smallest to largest. 2. Determine the value of n X 100. This value is used to find the position of the pth percentile in the ordered list.

If n X – 100 is not an integer, round it up to the next integer. The observation in this position is the pth percentile. c If n X – 100 is an integer, calculate the meanof the observations in this position and the next (higher) position. This mean is the pth percentile.

Method B:

To find a pth percentile of a sample of rz observations:

1. Order the n observations from smallest to largest. , 2. Determine the value of (n+1) X 100—. This value is used to find the position of the pth percentile in the ordered list.

• If (n+1) X — 100 is an integer, the observation in this position is a pth percentile. • If (n+1) X — 100 is not an integer but equal to k plus some proper fraction d, the pth percentile is a value lying d of the distance between the observations in the kth and (k+1)th positions.

This solution assists with the percentile problems attached. The mean of the observations in the position are calculated.