연구방법론  자료

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그룹

점수대(X)        빈도(f)      누적빈도(cum  f)

백분율

누적백분율

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1

330-334

4

4

  8%

    8%

2

335-339

5

9

10%

  18%

3

340-344

6

15

12%

  30%

4

345-349

9

24

18%

  48%

5

350-354

7

31

14%

  62%

6

355-359

7

38

14%

  76%

7

360-364

5

43

10%

  86%

8

365-369

4

47

  8%

  94%

9

370-374

3

50

  6%

100%

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III.  3.  김영희  학생의  백분위가  78%라면  그의  수능  평가점수는  얼마인가?

           

78%로  추정되는  점수대는  누적백분율을  참고해보면  360-364점에  해당될  것임

이  점수대의  하한계(Xll)는  359.5임.    또  어떤  누적%에  해당되는  누적빈도를  구하는 

공식은  --->  백분위에  해당되는  누적빈도=  해당  누적%  x  전체  사례  수(N)/100  임. 

그러므로  78%에  해당되는  누적빈도(cum  f)는  78  x  50/100  =  39

점수대의  간격은  5점,            78%로  추정되는  점수대의  빈도(fi)  =  5,   

추정되는  점수가  속하기  전  까지의  누적빈도  =  38 

이러한  정보를  공식  Xp  =  Xll  +  I(cum  f  –  cum  fll)/fi  에  대입해보면 

X78%  =  359.5  +  5(78x50/100  –  38)/5  =  360.5

*  참고:  하한계란  반올림해서  어떤  수가(값이)  될  수치(값)  중에서  가장  낮은 

소수점  단위(예  5의  하한계는  4.5이며  10의  하한계는  9.5임)

   

4.  이철수의  수능평가점수가  360.5라면  그의  백분위는  몇  %인가?

같은  맥락으로  이것을  공식  Px=  {cum  fll  +  [(X-  Xll)/i]  x  fi}/N  x  100에  대입하면

P360.5  =  {38  +  [(360.5-  359.5)/5]  x  5}/50  x  100  =  78%