# 25 and 75 Percentiles

There seems to be problem with 25 and 75 perentile values from the descriptive statistics function (linear). For the data set: 1, 2, 3, 4, 5, 6, 7, 8 statistiXL returns 2.25 (25%) and 6.75 (75%). Values should be 2.5 and 6.5, correct? Thanks

• Hi Kennic

There are many different ways to calculate percentiles. The well know main-frame descended stats package SAS for instance provides 5 different ways for calculating them. Your values are indeed appropriate for one such measure. The formula used by statistiXL however, is similar to that employed by the SPSS software package.

An excellent comparison of two of the most common methods, including that used by statistiXL/SPSS has been written by Dr. Russel John of Murdoch University in Western Australia and can be found here.

The basic calculation that statistiXL employs is as follows...

calculate the value p(n+1) where n=the number of samples and p=the percentile we want to calculate (eg 0.25 and 0.75 in your example)

now set k = the integer part of the above value
and a = the decimal or fractional part

the resultant percentile is then calculated as follows

If p < (1 / (n+ 1)) then the Percentile = x(1)
else If p > (n / (n + 1)) then the percentile = x(n)
else the percentile = (1 - a)X(k) + aX(k+1)

where X(k) = the kth value in your ordered dataset (eg X(2) = 2 in the sample you provide).

I hope this helps clear things up for you.

Best regards

Alan Roberts