Module 8
Assessment of Student Learning
Module 8
ORGANIZING ASSESSMENT DATA
Objectives

Arrange data in tables and graphs in a correct fashion

Present and interpret correctly data in a tabular or graphic format
Introduction
After scoring the test papers in a particular subject, more often than not
teachers are faced with a problem in interpreting the scores of their pupils. They find
difficulty on describing and synthesizing data that facilitates decision making. In this
lesson, we will attempt to present different ways of tabulating and graphing data.
Suppose we have just given a Math test to our Grade VI pupils. We have scored
the papers. What are we going to do with the data? Some of the question that we will
probably ask include “ What is the general pattern of the set of scores?, or ‘ What do
these scores look like?”, or “ How can we picture the set of scores to get an impression
of the group as a whole? To answer these questions, we will need to consider simple
ways of tabulating and graphing a set of scores.
The simplest rearrangement would be to just arrange the scores from highest to
lowest, but this simple arrangement of scores still has too much detail for us to
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Module 8
Assessment of Student Learning
understand general pattern clearly. We need to condense it into a more compact form
so that computation and interpretation would be easier.
Preparing a frequency distribution
One way of organizing the scores for presentation is to prepare what is termed
as a frequency distribution. This is table showing how often each score occurred. Each
score value is listed and the number of times it occurred is shown.
Steps in drawing a frequency distribution
a. Find the Range of the scores. The Range is the score distance between the
highest and the lowest scores.
Range = Highest score – Lowest Score
Example:
H.S.:
87
L.S.:
-42
45 Range
b. Decide on the number or size of the grouping. Grouping here refers to the
number of steps
Maximum number of grouping – 20
Minimum number of grouping – 7
Ideal number of grouping- 10-15
c. Determine the interval
Interval = Range
number of steps
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Assessment of Student Learning
Example: 45
10 = 4.5 or 5
d. Get the Lowest Limit (L.L.) of the step interval.
Divide the Lowest Score by the interval and then multiply by the interval
Example: 42
5 = 8 x 5 = 40
So the Lowest Limit is 40 – 44. There are five scores in this score interval namely:
40,41, 42, 43, and 44.
Remember that the Lowest Limit should be equal to the number that is
exactly divisible by the interval, so we round off the answer for (Lowest score
interval).
The finished Frequency Distribution should look like this.
Score interval
85-89
80-84
75-79
70-74
65-69
60-64
55-59
50-54
45-49
40-44
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Assessment of Student Learning
Illustrative example
A Math test is given to a class. Here are the scores of the 50 students. Let’s
make a frequency distribution and tally the frequency.
Scores
48
32
35
28
20
25
28
36
38
41
35
30
15
16
19
18
33
34
13
15
36
46
44
41
38
39
19
29
16
44
40
43
48
46
47
43
39
31
29
28
42
40
45
39
31
28
29
18
19
12
Solution:
1. The Range of the distribution is 36 ( HS-LS; 48-12=36)
2. Ideal number of grouping is 10
3. The Interval of the distribution is 4 (Range/10; 36/10 = 3.6 or 4)
4. The Lowest Limit of the distribution is 12 – 15 (Note that the lowest score (12) is
exactly divisible by the interval (4).
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Assessment of Student Learning
Frequency Distribution of Math Scores
Score Interval
48-51
44-47
40-43
36-39
32-35
28-31
24-27
20-23
16-19
12-15
Tally
II
IIII – I
IIII – II
IIII – II
IIII
IIII – IIII
I
I
IIII – II
IIII
Frequency
2
6
7
7
5
10
1
1
7
4
Remember that:
1. The Lowest score (12) is located on the lowest step or score interval (12-15).
Similarly, the highest score (48) is locate on the highest step or score interval
(48-51).
2. All number on the left (we call it lower limit) are exactly divisible by the
interval (4).
3. There are 10 step or score intervals (because we chose to divide the
distribution into ten. Nevertheless, there are instances that number of step
or score interval exceeds ten, especially when lowest score is not divisible by
the interval (product of rounding off numbers)
4. If no score falls on a particular step interval, the frequency for that step
interval is 0.
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Assessment of Student Learning
5. The frequency distribution provides not only a summary of the scores but it
is clearer what scores occurred most frequently, least frequently and the
relative performance of the whole group. That is: when higher number can
be found on the higher step interval, it means that most of the students got
high scores. Conversely, when most of the students got low scores, higher
frequencies can be found on the lower step or score intervals.
6. We can summarize even large number of scores in a frequency distribution
as short as the example given. For example, we can summarize a set of 1000
scores , and we can easily describe how the scores run from high to low, how
many obtained high and low scores, among the few important others.
Graphical Representation
It is often helpful to translate data into a pictorial representation. A common
type of graphic representation, which is called a histogram, is shown below.
10
9
Number of Cases
8
7
6
5
4
3
2
1
12-15
16-19
20-23
24-27
28-31
32-35
36-39
40-43
44-47
48-51
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The histogram can be thought of somewhat grimly, as “piling up the bodies”.
The score intervals are shown along the horizontal base line (abscissa). The vertical
height of the pile (ordinate) represents the number of cases. The diagram indicates that
there are four “bodies” piled up in the interval 12-15, seven in the interval 16-19, and so
forth. The figure gives a clear picture of how the piles up, with most of them in the 2831, while only few (only 2) got scores between 20-27
The left most part of the histogram represents the step or score interval where
lower scores can be located while the higher scores are located on the right most part of
the graph. As compared to frequency distribution, one can get quick information as to
what score interval did most scores fall, or least fall by simply looking at the piles.
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Assessment of Student Learning
Activity 1
a. Given the following scores, prepare a step distribution using 10 as the number of
grouping.
Scores
48
30
45
43
32
39
55
61
57
53
59
57
40
36
32
59
48
53
60
59
29
31
29
66
41
47
31
61
51
36
47
47
49
35
31
34
43
35
53
34
52
51
33
43
47
35
47
51
28
37
42
39
73
71
48
44
58
27
25
70
b. Translate the frequency distribution into a histogram
c. Answer the following questions.
1. In what step interval most scores fall?
2. Are there more students who got low or high scores?
3. Describe the relative performance of the whole class.
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Assessment of Student Learning
Activity 2. Share three important concepts/insights that you gained out of the lesson.
Briefly reflect on how these concepts/insights can help you become a more effective
teacher.
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