% Illustartion of standard deviation function main()    a=-1.2; b = 1.3;    c = -0.5; d = 2.5;    N=100;        X=linspace(a, b, N);    Y=X.^3-0.2*X.^2-X+2; %   Y=X.^2;        % scale Y to fit in the plotting window    Y = (Y-min(Y))/(max(Y)-min(Y));    Y = Y*(d-c)+c;        mean = sum(Y)/length(Y);    stdev = sqrt(sum((Y-mean).*(Y-mean))/length(Y));        figure(1); clf; hold on; axis off; axis equal;        lw = 3; % linewidth    lw2 = lw/2;    lw3 = lw/1.5;    fs = 30; % font size    red=[0.867 0.06 0.14];    blue = [0, 129, 205]/256;    green = [0, 200,  70]/256;    black = [0, 0, 0];     % plot the curves    shiftl=a-0.1;    small=0.2;    plot(X, Y, 'linewidth', lw, 'color', blue);    plot([shiftl max(X)+small], [mean, mean], 'linewidth', lw2, 'color', red);    plot([shiftl max(X)+small], [mean, mean]+stdev, 'linewidth', lw3, 'color', red, 'linestyle', '--');    plot([shiftl max(X)+small], [mean, mean]-stdev, 'linewidth', lw3, 'color', red, 'linestyle', '--');  % plot some balls for beauty    n = length(X);    ball_rad = 0.03;    ball(X(1), Y(1), ball_rad, blue)    ball(X(n), Y(n), ball_rad, blue)     % axes    small=0.2;    arrowsize=0.2; arrow_type=0;    angle=20; % in degrees     arrow([shiftl-0.2 0], [b+0.2, 0],             lw2, arrowsize, angle, arrow_type, black)    arrow([shiftl, min(Y-0.1)], [shiftl, max(Y)], lw2, arrowsize, angle, arrow_type, black)  % text    small1 = 0.3; small2 = 0.3;    text(shiftl-small1, mean,  '\mu', 'fontsize', fs)    text(shiftl-small1-small2, mean+stdev,  '\mu+\sigma', 'fontsize', fs)    text(shiftl-small1-small2, mean-stdev,  '\mu-\sigma', 'fontsize', fs) %   H=text(0.1, -0.1,  'x_{n+1}'); set(H, 'fontsize', fs) %   H=text(0.7, -0.1,  'x_{n}'); set(H, 'fontsize', fs)  % save to disk    saveas(gcf, 'Standard_deviation.eps', 'psc2') %   plot2svg('Standard_deviation.svg');  function arrow(start, stop, thickness, arrow_size, sharpness, arrow_type, color)  % Function arguments: % start, stop:  start and end coordinates of arrow, vectors of size 2 % thickness:    thickness of arrow stick % arrow_size:   the size of the two sides of the angle in this picture -> % sharpness:    angle between the arrow stick and arrow side, in degrees % arrow_type:   1 for filled arrow, otherwise the arrow will be just two segments % color:        arrow color, a vector of length three with values in [0, 1]  % convert to complex numbers    i=sqrt(-1);    start=start(1)+i*start(2); stop=stop(1)+i*stop(2);    rotate_angle=exp(i*pi*sharpness/180);  % points making up the arrow tip (besides the "stop" point)    point1 = stop - (arrow_size*rotate_angle)*(stop-start)/abs(stop-start);    point2 = stop - (arrow_size/rotate_angle)*(stop-start)/abs(stop-start);     if arrow_type==1 % filled arrow  % plot the stick, but not till the end, looks bad       t=0.5*arrow_size*cos(pi*sharpness/180)/abs(stop-start); stop1=t*start+(1-t)*stop;       plot(real([start, stop1]), imag([start, stop1]), 'LineWidth', thickness, 'Color', color);  % fill the arrow       H=fill(real([stop, point1, point2]), imag([stop, point1, point2]), color);       set(H, 'EdgeColor', 'none')     else % two-segment arrow       plot(real([start, stop]), imag([start, stop]),   'LineWidth', thickness, 'Color', color);       plot(real([stop, point1]), imag([stop, point1]), 'LineWidth', thickness, 'Color', color);       plot(real([stop, point2]), imag([stop, point2]), 'LineWidth', thickness, 'Color', color);    end      function ball(x, y, r, color)    Theta=0:0.1:2*pi;    X=r*cos(Theta)+x;    Y=r*sin(Theta)+y;    H=fill(X, Y, color);    set(H, 'EdgeColor', 'none');