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. 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. The following measures of
relative standing that shall be
explored in this chapter are
the following
◦Quartile
◦Decile
◦Percentile
◦Percentile rank
◦Z score
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. 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. ◦ 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. 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. 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
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. 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. 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
