2.6 MEASURES OF POSITION

z-Scores and Percentiles

z-Scores

- enable standardize values & compare difference sets of scores  
Sample   Population 

 

 
 #2
 
 
 

  #6
 
 
 

   #10     Comparison
 
 
 
 
 

Values within two z- scores are "usual"   but 2 is unusual  ( diagram pg 93)
 

Quartiles, Deciles, and Percentiles

 
Quartiles  --  Divide into 4 similar to median dividing into 2
 
Deciles  -- Divides into 10 pieces 
 
Percentiles  --  Divides into 100 parts 
 
         88 Percentile means Student's score is higher than or = 88% of the scores
 
 
 
 
  
Find the Percentile of a particular score

Example:  Use temperatures entered into calculator list from end of Chapter 1 and
                         sorted into ascending order -

            97.6 degrees      is 17/106 = 0.16       which is 16th percentile
 
 
             What percentile is 98.5 Degrees
 
 

REVERSE -  What scores is at  k__ percentile

          Find  k %  of the total number  =  L

         a)  If L is not a whole number, round up and find the score in position L
  or   b)  If L is a whole #, find the average of the scores in positions L and L+1
 
 
From temperatures entered at end of chapter 1