Atanas -

Excel assigns cumulative relative frequency of zero to the minimum value of
the data set and cumulative relative frequency of one to the maximum value.
Intermediate values of the data set are assigned cumulative relative
frequency in steps of 1/(n-1), where n is the number of values in the data
set.

To determine intermediate percentiles, Excel uses linear interpolation
between two cumulative relative frequencies.

For n=4, the four values are assigned cumulative relative frequencies 0.0,
0.33333..., 0.66666..., and 1.0.

The 3rd quartile has cumulative relative frequency 0.75. The interpolation
between your data values 1.22 and 3.11 is
1.22+(3.11-1.22)*(0.75-0.66667)/(1.0-0.66667) = 1.22+1.89*0.08333/0.33333 =
1.22+1.89*0.25 = 1.22+0.47 = 1.69.

- Mike Middleton
http://www.DecisionToolworks.com
Decision Analysis Add-ins for Excel



"Atanas" wrote in message
...
I know the definition of 3rd quartile and I know the formula in excel but
could not figure out how excel calculates it so I can explain it at my
trial.
My population is relatively small 1.22x, 1.12x, 3.11x and 0.85x. the
median
is 1.17x the 1st quartile is 1.05x and the 3rd quartile is 1.69x. I tried
to
figure out how excel calculates these quartiles when the population is not
big enough. I really appreciate your help and thank you in advance.