Sigurado ako by now, may nakapagsabi na sayo yung technique na ginagawa nila pag multiple choice yung exam. Most likely, eto yun:

When in doubt, choose b or c.

Sinabi din to samin nung prof ko dati. Since yung sa board exam nga daw ay automated yung pagpili ng questions sa database. So automated din daw yung pag lalagay nung position nung Correct answer sa choices.

In an attempt to prove the theory na may preference yung pag-automate sa b and c na answer...
-Gumawa ako ng program na nagrarandomize ng number from 1 to 4. 1 represents a, 2 for b, 3 for c and 4 for d. Simulating yung correct letter of answer.
-I made it to simulate the board exam na gumagawa ng 100 questions.
-ni-simulate ko din na gumawa ng 50 exams yung program.
-Kinuha ko yung Mean, Median, at Relative Frequency Distribution per batch.
-1 batch = 1 run of the program
-I took 5 batches.

Eto yung source code: Click on the Text Area, press CTRL+A, then CTRL+C to copy the source code
#include<iostream.h> #include<conio.h> #include<stdlib.h> #include<time.h> #include<iomanip.h> float findmedian(int x[50]); void sort(int x[50]); void frequency(int f[4][6], int x[50], int i); void variance(float s[], int x[50], float average[], int i); void variance(float s[], int x[50], float average[], int i) { int a; float m[50], n[50], sum=0.0; for(a=0; a<50; a++) { m[a]=x[a]-average[i]; n[a]=m[a]*m[a]; sum=sum+n[a]; } s[i]=sum/49; } void frequency(int f[4][6], int x[50], int i) { int j, a; for(j=0; j<50; j++) { if(x[j]>10&&x[j]<16) a=0; else if(x[j]>15&&x[j]<21) a=1; else if(x[j]>20&&x[j]<26) a=2; else if(x[j]>26&&x[j]<31) a=3; else if(x[j]>30&&x[j]<36) a=4; else if(x[j]>35) a=5; f[i][a]++; } } void sort(int x[50]) { int temp, i, j, a; for(i=0; i<50; i++) { temp=0; j=i; while(j<50) { if (x[j]>temp) { temp=x[j]; a=j; } j++; } x[a]=x[i]; x[i]=temp; } } float findmedian(int x[50]) { sort(x); float median; median=(x[24]+x[25])/2; return median; } main() { int a[50], b[50], c[50], d[50], key; float sum, average[4], median; clrscr(); randomize(); for(int i=0; i<50; i++) { a[i]=0; b[i]=0; c[i]=0; d[i]=0; for(int j=0; j<100; j++) { do key=random(5); while(key==0); switch (key) { case 1: a[i]++; break; case 2: b[i]++; break; case 3: c[i]++; break; case 4: d[i]++; } } if (i>0&&i%2!=0) cout<<"\t"; cout<<"Trial "<<i+1<<": "; if (i<9) cout<<" "; cout<<"a="<<a[i]<<" b="<<b[i]<<" c="<<c[i]<<" d="<<d[i]; if (i>0&&i%2!=0&&i!=49) cout<<endl; } getch(); clrscr(); cout<<endl<<endl; cout<<"Average incidence of Answers after 50 trials of 100 questions:"<<endl<<endl; for(i=0; i<4; i++) { sum=0; for(int j=0; j<50; j++) { switch (i) { case 0: sum=sum+a[j]; break; case 1: sum=sum+b[j]; break; case 2: sum=sum+c[j]; break; case 3: sum=sum+d[j]; } } average[i]=0.0; average[i]=sum/50; switch (i) { case 0: cout<<"A="; break; case 1: cout<<" B="; break; case 2: cout<<" C="; break; case 3: cout<<" D="; } cout<<average[i]<<setprecision(2)<<"%"; } cout<<endl<<endl; cout<<"Median after 50 trials"<<endl<<endl; for(i=0; i<4; i++) switch (i) { case 0: median=findmedian(a); cout<<"A="<<median; break; case 1: median=findmedian(b); cout<<" B="<<median; break; case 2: median=findmedian(c); cout<<" C="<<median; break; case 3: median=findmedian(d); cout<<" D="<<median; } cout<<endl<<endl; getch(); clrscr(); cout<<"A\tB\tC\tD"<<endl; for(i=0; i<50; i++) { cout<<a[i]<<"\t"<<b[i]<<"\t"<<c[i]<<"\t"<<d[i]<<endl; if(i==25) getch(); } getch(); clrscr(); cout<<endl<<endl<<endl; int f[4][6]; for(i=0; i<4; i++) { for(int j=0; j<6; j++) f[i][j]=0; switch (i) { case 0: frequency(f, a, i); break; case 1: frequency(f, b, i); break; case 2: frequency(f, c, i); break; case 3: frequency(f, d, i); } } cout<<"Relative Frequency Distribution"<<endl; cout<<"\tA\t\tB\t\tC\t\tD"<<endl; cout<<"Range\tExams\t%\tExams\t%\tExams\t%\tExams\t%"<<endl; for(i=0; i<6; i++) for(int j=0; j<4; j++) { if(j==0) switch (i) { case 0: cout<<"11-15\t"; break; case 1: cout<<"16-20\t"; break; case 2: cout<<"21-25\t"; break; case 3: cout<<"26-30\t"; break; case 4: cout<<"31-35\t"; break; case 5: cout<<">35\t"; } float percentage=0.0; percentage=f[j][i]/50.0; cout<<f[j][i]<<"\t"<<percentage<<setprecision(2); if(j<3) cout<<"\t"; else cout<<endl; } getch(); clrscr(); float s[4]; for(i=0; i<4; i++) switch (i) { case 0: variance(s, a, average, i); break; case 1: variance(s, b, average, i); break; case 2: variance(s, c, average, i); break; case 3: variance(s, d, average, i); } cout<<"Variance"<<endl; cout<<"A="<<s[0]<<" B="<<s[1]<<" C="<<s[2]<<" D="<<s[3]; getch(); return 0; }

Eto ang results...

Data

so ayan sa taas yung 5 batches ng data

Mean and Median

So as you can see, sa limang batches ng 50 exams, magkakalapit lang yung mean at median nung apat na sagot. Ibig sabihin walang preference sa b at c na sagot. halos pantay pantay lang yung incidence nung mga sagot.

Relative Frequency Distribution

In general, pinakacommon yung 21-25 number range for all choices. Pumapangalawa yung 26-30. Or baliktad dun sa iba. Pero pwede natin maconclude na mataas yung frequency from the 21-30 range. Population mean is 25.5, so safe assumption na 25 questions na ang sagot ay isa sa choices out of 100 questions. Tig te-25 ang a, b, c at d.

Conclusion
Walang katotohanan yung preference sa multiple choice na b and c sa board exam. Of course, ako kasi yung nagsulat ng program na ito at wala akong nilagay na segment na magkakaron ng preference sa choices.

Meron akong theory kung totoo man yung preference sa b and c. Pag hindi automated or manual yung pag sulat nung choices, ang mindset, itago sya sa gitna, which are b and c.

Eto yung human factor in making the exam. Akala lang ng tao random nya ginagawa pero subconsciously, may pattern syang nagagawa or yung mindset nga sa gitna ilagay.

Kaya kung totoo yung preference ng b and c sa board exam, in my opinion, hindi automated yung pag jumble nung choices. Malamang, random lang yung questions. Pero kasamang ini-input yung choices dun sa database. Kaya pag napili nung computer yung question, kung pano ininput yung choices sa database, ganun na sya i-a-output.

Isa lang ang paraan para maconfirm natin to. Kung ipapakita yung source code nung Question Randomizer na ginagamit for the board exam, matetrace kung meron ngang preference segment. Pero asa naman na ipapakita saken yun!