Assessment in Learning

1. TOPIC-LESSON 8: ANALYSIS,
INTERPRETATION, AND USE OF
TEST DATA
Demo Reporters:
Marlene A. Talde
Vina Torres
Hazel M. Tabayay
Nian Rose G. Roquina

2. DESIRED SIGNIFICANT LEARNING OUTCOME
In this lesson, you are expected to: Analyze, Interpret, and use test data
applying
Measure of Central Tendency,
Measures of Variability
Measures of position, and
Measures of Co - variability

3. Significant Culminating Performance task and success Indicators
At the end of the lesson, you are expected to analyze test scores using the
measures of central tendency, variability, position and co-variability.
Understanding of these measures is helpful to know to improve teaching. Your
success in this performance will be determined if you have done the following.

4. TASKS SUCCESS INDICATORS
Calculate the mean,median and make de of test scores from the given set of
test scores
From own and actual set of test data,compute at least two measures of central
tendency in two days.
Write a general statement of interpretation from computer mean,median and
mode of test data, and the relationship of the three measures and shape the
skewness of the test distribution of scores
Give at least three interpretation statements of your own test work output
aligned with the assessment objectives.
Identify the level of measurement for a given variable Explain in a statement or two the level of measurement that applies to variable
measured by your own test data.
Explain the concept of variability on test results and calculate the different
measures of variability
From own test data sheet,compute the standard deviation and give a statement
or two to describe the test results on the basis of such measures
Explain how measures of variability relate to skewness and kurtosis of
frequency polygon of test data
Present empirical evidence of how measures of variation affects the shape of
frequency of polygon of test scores.
Determine the different measures of position Apply the different measures of positions in interpreting test scores in a
distribution.
Covert raw scores in standard scores Use standard scores to compare two scores in a distribution in at least two
practical and real teaching-learning situations.
Determine the measures of co-variability between two tests From a given test data, compute the occurrence of co-variability of two test
scores.

5. PREREQUISITE OF THIS LESSON
The discussion in this lesson, will build upon the concepts and examples
presented in Lesson 7, Which focused on the tabular and graphical presentation
and interpretation of test results.In this Lesson, other ways of summarizing test
data using descriptive statistics, which provides a more precise means of
describing a set of scores will be discussed. The word “measures” is commonly
associated with numerical and quantitative data.Hence, the prerequisite to
understanding the concepts contained in this lesson is your basic knowledge
and mathematics,. e.g., summation of values, simple operations on integers,
squaring and finding the square roots, and etc.

6. WHAT ARE MEASURES OF CENTRAL TENDENCY?
Means the central location or point of convergence of a set of values.
Test scores have a tendency to convergence of a central value.
The value is the average of the set of scores.
Three commonly-used measures of central tendency of measures of central location are the MEAN,
MEDIAN, and the MODE.
MEAN
Most preferred measures of central tendency for use with test scores.
Also referred to as the arithmetic mean.
The computation is very simple.
That is, X= [X Where X = the mean,
N
[X= the sum of all the scores, and N = the number of scores in the set.
Consider again the test scores of students given in table 8.1 which is the same set of test scores in
the previous lesson.

7. Table 8.1 Scores of 100 College student in a final
examination
53 30 21 42 33 41 42 45 32 58
36 51 42 49 64 46 57 35 45 51
57 38 49 54 61 36 53 48 52 49
41 58 42 43 49 51 42 50 62 60
33 43 37 57 35 33 50 42 62 49
75 66 78 52 58 45 53 40 60 33
46 45 79 33 46 43 47 37 33 64
37 36 36 46 41 43 42 47 56 62
50 53 49 39 52 52 50 37 53 40
34 43 43 57 48 43 42 42 65 35

8. Table 8.1 Scores of 100 College student in a final
examination
53 30 21 42 33 41 42 45 32 58
36 51 42 49 64 46 57 35 45 51
57 38 49 54 61 36 53 48 52 49
41 58 42 43 49 51 42 50 62 60
33 43 37 57 35 33 50 42 62 49
75 66 78 52 58 45 53 40 60 33
46 45 79 33 46 43 47 37 33 64
37 36 36 46 41 43 42 47 56 62
50 53 49 39 52 52 50 37 53 40
34 43 43 57 48 43 42 42 65 35
The mean is the sum of all the scores from 53
down to the last score, which is 35.
That is, X= [X = 53+36++57……..+60+49+35
N

9. Table 8.2 Frequency Distribution of Grouped Test Scores
Class Interval Midpoint (X) f Xi F Cumulative Frequency(cf) Cumulative Percentage
75-80 77 3 231 100 100
70-74 72 0 0 97 97
65-69 67 2 134 97 97
60-64 62 8 496 95 95
55-59 57 8 456 87 87
50-54 52 17 884 79 79
45-49 47 16 846 62 62
40-44 42 21 882 44 44
35-39 37 13 481 23 23
30-34 32 9 288 10 10
25-29 27 0 0 1 1
20-24 22 1 22 1 1
Total (N) 100 [Xi f=4720

10. In the traditional way, it cannot be argued that you can see at a glance how the scores are
distributed among the range of values in a condensed manner. You can even estimate the
average of the scores by looking at the frequency in each class interval. In the absence of
statistical program the mean can be computer by the following formula:
X = [Xi f
N
Where Xi = midpoint of the class interval
F = frequency of each interval
N = total frequency
Thus, the mean on the test scores in table 7.1 is calculated as follows:
X= [Xi f = 4720 = 47.2
N 100
MEDIAN
The value that divides the ranked score into halves, or the middle value of the ranked
scores.
If the number of scores is odd, then there is only one middle value that gives the median.
However, if the number of scores in the set is an even number, then there are two middle
values.

11. Table 8.2 Frequency Distribution of Grouped Test Scores
Class Interval Midpoint (X) f Xi F Cumulative
Frequency(cf)
Cumulative Percentage
75-80 77 3 231 100 100
70-74 72 0 0 97 97
65-69 67 2 134 97 97
60-64 62 8 496 95 95
55-59 57 8 456 87 87
50-54 52 17 884 79 79
45-49 47 16 846 62 62
40-44 42 21 882 44 44
35-39 37 13 481 23 23
30-34 32 9 288 10 10
25-29 27 0 0 1 1
20-24 22 1 22 1 1
Total (N) 100 [Xi f=4720
This formula will help you to determine the median:
Mdn = lower limit + size of the class interval of median
class
[(n) --- cumulative frequency below the median class)
2 frequency of the median class

12. MODE
The easiest measure of central tendency to obtain.
It is the score or value with the highest frequency. In the set of scores.
If the score are arranged in a frequency distribution, the mode is estimated as the
midpoint of the class interval which has the highest frequency.
This class interval with the highest frequency is also called the modal class.
To appreciate comparison of the three measures of central tendency, a brief
background of level measurement is important.
The level of measurement helps you decide how to interpret the data as measures of
these attributes, and this serves as the guide in determining in part the kind of
descriptive statistics to apply in analyzing the test data.

13. SCALE OF MEASUREMENT
There are four levels of measurement that apply to be treatment of test data:
nominal, ordinal, interval, and ratio.
1. NOMINAL
The number is used for labelling or identification purposes only.
Example: student’s identification number or section number.
2. ORDINAL
It is used when the values can be ranked in some order of characteristics.
The numeric values used is indicate the difference in traits under consideration.
Example: academic awards are made on the basis of an order of performance:
first honor, second honor, third honor, and so on.

14. 3. INTERVAL
Which has the properties of both nominal and ordinal scales.
Attained when the values can describe the magnitude of the differences
between groups or when the intervals between the numbers are equal.
“Equal interval “means that the distance between the things represented by
3 and 4 is as the same distance represented by 4 and 5.
Example: the most common example of interval scale is temperature
readings.
(The difference between the temperatures 30*and 40*is the same as that
between 90* and 100*)
4. RATIO
It the highest level of measurement.
As such, it carries the properties of the nominal,ordinal,and interval scales.
Its additional advantage is the presence of a true zero point, where zero
indicates the total absence of the trait being measured.

15. HOW DO MEASURE OF CENTRAL TENDENCY DETERMINE SKEWNESS?
SYMMETRICAL DISTRIBUTION
- the mean, median, and mode have the same value, and the value of the
median is between the mean and the mode
Y
X

16. POSITIVELY-SKEWED DISTRIBUTION
-the mode stays at the peak of the curve and its value will be smallest.
- the mean will be pulled out from the peak of the distribution toward the
direction of the few high scores.
Thus, the mean gets the largest value. The median is between the mode and
the mean.

17.  NEGATIVELY-SKEWED DISTRIBUTION
-the mode remains and the peak of the curve, but it will have the largest
value.
-the mean will have the smallest values as influenced by the extremely low
scores, and the median still lies between the mode and the mean.