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//Cpation: Bowley's Measure of Skewness
//Example3.19
//Page63
clear;
clc;
X = [0,4;4,8;8,12;12,16;16,20;20,24;24,28;28,32];//Machine breakdown time (hrs)
f = [26,50,70,80,100,60,50,24]; //No. of machines
cum_f = cumsum(f);//cumulative frequencies
N = sum(f); //total frequency
C = diff(X(1,:)); //class interval
cen1 = N/4;
cen2 = N/2;
cen3 = 3*N/4;
for i = 1:length(f)
if ((cum_f(i)< cen1) &(cen1< cum_f(i+1))) then
L1 = X(i+1,1);
f1 = f(i+1);
F1 = cum_f(i)
C = diff(X(i+1,:));
end
if ((cum_f(i)< cen2) &(cen2< cum_f(i+1))) then
L2 = X(i+1,1);
f2 = f(i+1);
F2 = cum_f(i)
end
if ((cum_f(i)< cen3) &(cen3< cum_f(i+1))) then
L3 = X(i+1,1);
f3 = f(i+1);
F3 = cum_f(i)
C = diff(X(i+1,:));
end
end
disp(L1,'Lower limit of the first quartile class L1 =')
disp(f1,'Frequency of the first quartile class f1 =')
disp(F1,'Cumulative frequency of the previous class w.r.to the first quartile class F1=')
disp(C,'Width of the class interval C=')
Q1 = L1+(((N/4)-F1)*C/f1);
disp(Q1,'Fist Quartile Q1=')
disp(L2,'Lower limit of the second quartile class L2 =')
disp(f2,'Frequency of the second quartile class f2 =')
disp(F2,'Cumulative frequency of the previous class w.r.to the second quartile class F2=')
disp(C,'Width of the class interval C=')
Q2 = L2+(((N/2)-F2)*C/f2);
disp(Q2,'Fist Quartile Q1=')
disp(L3,'Lower limit of the third quartile class L3 =')
disp(f3,'Frequency of the third quartile class f3 =')
disp(F3,'Cumulative frequency of the previous class w.r.to the third quartile class F3=')
disp(C,'Width of the class interval C=')
Q3 = L3+(((3*N/4)-F3)*C/f3);
disp(Q3,'Third Quartile Q3=')
CS = (Q3+Q1-2*Q2)/(Q3-Q1)
disp(CS,'Bowleys coefficient of skewness CS=')
//Result
//
// Lower limit of the first quartile class L1 =
//
// 8.
//
// Frequency of the first quartile class f1 =
//
// 70.
//
// Cumulative frequency of the previous class w.r.to the first quartile class F1=
//
// 76.
//
// Width of the class interval C=
//
// 4.
//
// Fist Quartile Q1=
//
// 10.228571
//
// Lower limit of the second quartile class L2 =
//
// 16.
//
// Frequency of the second quartile class f2 =
//
// 100.
//
// Cumulative frequency of the previous class w.r.to the second quartile class F2=
//
// 226.
//
// Width of the class interval C=
//
// 4.
//
// Fist Quartile Q1=
//
// 16.16
//
// Lower limit of the third quartile class L3 =
//
// 20.
//
// Frequency of the third quartile class f3 =
//
// 60.
//
// Cumulative frequency of the previous class w.r.to the third quartile class F3=
//
// 326.
//
// Width of the class interval C=
//
// 4.
//
// Third Quartile Q3=
//
// 21.266667
//
// Bowleys coefficient of skewness CS=
//
// - 0.0747196
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