There are occasions when teachers are interested in describing the relative position of a student’s scores obtained by the whole class. This chapter is focused on the different measures of relative standing. According to Sincich (1993), 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. The following measures of relative standing that shall be explored in this chapter are the following: quartile; decile; percentile rank; and Z score.
Quartile
Quartile ) is a point measure that divides a distribution into four equal parts (Freud & Simon, 1997). The first or lower quartile ) separates the bottom 25% of the scores. Thus, 25% of scores fall below Q1, Q1 is the equivalent to the median, while the third or upper quartile separates the 25% from the bottom 75% of the scores. It follows that 25% of scores fall above Q3 and 75% below it.
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 .
3. Look for the cumulative frequency that approximates . The class above it is the 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 following computational formula:
f
Where: = exact lower limit of the Q1 class
= locator of the Q1 class
= total number of scores
= cumulative frequency before the Q1 class
= frequency of the Q1 class
= class size
Shown in Table 14.1 is the computation of Q1
TABLE 14.1
Computation of the First
or Lower Quartile
| Classes | Frequency | Cumulative Frequency |
| 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 | |
Q1 class = 40 – 44
CF = 11 f = 7 L = 39.5 = 5
Q1 class = 40 – 44 CF = 11 f = 7
L = 39.9 = 5
f
7
= 41.64
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 distribution by dividing 3N by
3. Look for the cumulative frequency that approximates . The class above it is the Q3 class.
4. Get the exact lower limit and frequency of the Q3 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 following computational formula:
f
Where: = exact lower limit of the Q1 class
= locator of the Q1 class
= total number of scores
= cumulative frequency before the Q1 class
= frequency of the Q1 class
= class size
The computational procedures in determining Q3 are illustrated in Table 14.2.
TABLE 14.2
Computation of the Third
Or Upper Quartile
| Classses | Frequency | Cumulative Frequency |
| 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 | |
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