quartile.m

% define data set
x = [16, 22, 24, 24, 27, 28, 29, 30]';
Nx = size(x,1);

% compute mean
mx = mean(x);

% compute the standard deviation
sigma = std(x);

% compute the median
medianx = median(x);

% STEP 1 - rank the data
y = sort(x);

% compute 25th percentile (first quartile)
Q(1) = median(y(find(y<median(y))));

% compute 50th percentile (second quartile)
Q(2) = median(y);

% compute 75th percentile (third quartile)
Q(3) = median(y(find(y>median(y))));

% compute Interquartile Range (IQR)
IQR = Q(3)-Q(1);

% compute Semi Interquartile Deviation (SID)
% The importance and implication of the SID is that if you 
% start with the median and go 1 SID unit above it 
% and 1 SID unit below it, you should (normally) 
% account for 50% of the data in the original data set
SID = IQR/2;

% determine extreme Q1 outliers (e.g., x < Q1 - 3*IQR)
iy = find(y<Q(1)-3*IQR);
if length(iy)>0,
    outliersQ1 = y(iy);
else
    outliersQ1 = [];
end

% determine extreme Q3 outliers (e.g., x > Q1 + 3*IQR)
iy = find(y>Q(1)+3*IQR);
if length(iy)>0,
    outliersQ3 = y(iy)
else
    outliersQ3 = [];
end

% compute total number of outliers
Noutliers = length(outliersQ1)+length(outliersQ3);

% display results
disp(['Mean:                                ',num2str(mx)]);
disp(['Standard Deviation:                  ',num2str(sigma)]);
disp(['Median:                              ',num2str(medianx)]);
disp(['25th Percentile:                     ',num2str(Q(1))]);
disp(['50th Percentile:                     ',num2str(Q(2))]);
disp(['75th Percentile:                     ',num2str(Q(3))]);
disp(['Semi Interquartile Deviation:        ',num2str(SID)]);
disp(['Number of outliers:                  ',num2str(Noutliers)]);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Percentile Calculation Example
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% define percent
kpercent = 75;

% STEP 1 - rank the data
y = sort(x);

% STEP 2 - find k% (k /100) of the sample size, n.
k = kpercent/100;
result = k*Nx;

% STEP 3 - if this is an integer, add 0.5. If it isn't an integer round up.
[N,D] = rat(k*Nx);
if isequal(D,1),               % k*Nx is an integer, add 0.5
    result = result+0.5;
else                           % round up
    result = round(result);
end

% STEP 4 - Find the number in this position. If your depth ends 
% in 0.5, then take the midpoint between the two numbers.
[T,R] = strtok(num2str(result),'0.5');
if strcmp(R,'.5'),
    Qk = mean(y(result-0.5:result+0.5));
else
    Qk = y(result);
end

% display result
fprintf(1,['\nThe ',num2str(kpercent),'th percentile is ',num2str(Qk),'.\n\n']);