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Chapter 14

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Chapter 14

  1. 1. CHAPTER 14 SUMMARIZING TEST SCORES: MEASURES OF RELATIVE STANDING
  2. 2. There vare occasions when teachers are interested in describing the relative position of student’s score in relation to scores obtained by the whole class.
  3. 3. Measures of relative standing- are descriptive measures that locate the relative position of a test score in relation to the other scores obtained by a group of students or test takers.
  4. 4. The following measures of relative standing that shall be explored in this chapter are the following ◦Quartile ◦Decile ◦Percentile ◦Percentile rank ◦Z score
  5. 5.  Quartile ◦ Is a point measure that divides a distribution into four equal parts(Freud and Simon,1997). The first or lower quartile(Q1) separates the bottom 25% from the top 75% of the scores. Thus, 25% of scores fall below Q1. Q2 is the equivalent to the median, while the third or upper quartile (Q3) separates the top 25% from the bottom 75% of the scores. It follows that 25% of scores fall above Q3 and 75% below it.
  6. 6.  In computing Q1 for grouped test scores, the following steps have to be observed(Weiss,1997). ◦ 1. Cumulate the frequencies from the lowest to the highest class interval. ◦ 2. Determine one-fourth or 25% of the number of test scores in the grouped frequency distribution by dividing N by
  7. 7. ◦ 3. Look for the cumulative frequency that approximates N/4. the class above it is Q1 class. ◦ 4. Get the exact lower limit and frequency of the Q1 class. ◦ 5. Get the total number of scores (N) and the class size. ◦ 6. Substitute all obtained values from step 2 to step 5 into the follwing computational formula:
  8. 8. Where:  L= exact lower limit of the Q1 class  N/4 = locator of the Q1 class  N= total number of scores  CF= cumulative frequency before the Q1 class  f= frequency of the Q1 class  i= class size
  9. 9. Table 14.1 Computation for the First or Lower Quartile Classes Frequency (f) Cumulative Frequency (CF) 60-64 55-59 50-54 45-49 40-44 35-39 30-2 5 8 10 15 7 6 5 56 51 43 33 18 11 5 N= 56
  10. 10. CF= 11 f= 7 Q1 CLASS= 40-44 L= 39.5 i= 5 Q1 class= 40-44 L=39.5 CF= 11 i= 5 f= 7
  11. 11. = 41.64
  12. 12.  The procedures in computing the third or upper quartile are as follows: ◦ 1. cumulate the frequencies from the lowest to the highest class interval. ◦ 2. determine three- fourths or 75% of the number of test scores In the grouped frequency that approximates 3N by ◦ 3. look for the cumulative frequency that approximates .The class above it is the Q3 class.
  13. 13.  4. get the exact lower limit and frequency of the Q3 class.  Get the total number of scores (N) and the class size.  Substitute all obtained values from step 2 to step 5 into the following computational formula:
  14. 14.  Where:  L= exact lower limit of the Q3 class  3N/4= locator of the Q3 class  N= total number of scores  CF= cumulative frequency before the Q3 class  f= frequency of the Q3 class  i= class size

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