Roel Q. Maramara

2. Roel maramara
bsned-sped

3. ASSESSMENT OF LEARNING

4. •Audio-visual aids are defined as any devices used to aid in the
communication of an idea. As such, virtually anything can be used as
an audio-visual aid provided it successfully communicates the idea or
information for which it is designed.
•An audio-visual aid includes still photography, motion picture, audio
or video tape, slide or filmstrip, that is prepared individually or in
combination to communicate information or to elicit a desired audio
response.
EDUCATIONAL TECHNOLOGY

5. Device is any means other than the
subject-matter itself that is employed by
the teacher in presenting the subject
matter to the learner
Device

6. 1. To challenge students’ attention
2. To stimulate the imagination and develop the mental
imagery of the pupils
3. To facilitate the understanding of the pupils
4. To provide motivation to the learners
5. To develop the ability to listen
Purpose of Visual Devices

7. 1. Demonstration
2. Field trips
3. Laboratory experiments
4. Pictures, films, simulations, models
5. Real objects
Traditional Visual Aids

8. 1. Extrinsic – used of supplement a method used. Example: pictures, graph,
dim strips, slides, etc.
2. Intrinsic – used as a part of the method or teaching procedures.
Example: pictures accompanying an article.
3. Material Devices – device that have no bearing on the subject matter.
Example: blackboard, chalk, books, pencils, etc.
4. Mental Devices – a kind of device that is related in form and meaning to
the subject matter being presented. Example: questions, projects, drills,
lesson plans, etc.
Classification of Devices

9. Non-projected aids are those that do not require the
use of audio-visual equipment such as a projector and
screen. These include charts, graphs, maps,
illustrations, photographs, brochures, and handouts.
Charts are commonly used almost everywhere.
NON-PROJECTED AUDIOVISUAL AIDS

10. It focuses on the development and utilization of
assessment tools to improve the teaching-learning
process. It on the use of testing for measuring knowledge,
comprehension emphasizes and other thinking skills. It
allows the students to go through the standard steps in
test constitution for quality assessment. Students will
experience how to develop rubrics for performance-based
and portfolio assessment.
ASSESSMENT OF LEARNING

11. - Refers to the quantitative aspect of evaluation. It involves
outcomes that can be quantified statistically. It also be
defined as a process in determining and differentiating the
information about the attributes or characteristics of things.
Measurement

12. -Is the quantitative aspect of determining the outcomes pf
learning. It involves value judgement. Evaluation is more
comprehensive than measurement.
-In fact, measurement is one aspect of evaluation.
Evaluation

13. - Consist of questions or exercises or other
devices for measuring the outcomes pf
learning.
Test

14. 1.According to manner of response
a. Oral
b. Written
2. According to method of preparation
a. Subjective / essay
b. Objective
3. According to the nature of answer
a. Personality tests
b. Intelligence test
c. Aptitude test
d. Achievement or summative test
e. Sociometric test
f. Diagnostic or formative test
g. Trade or vocational test
CLASSIFICATION OF TESTS

15. Objective tests are tests which have definite answers and therefore are not subject to
personal bias.
Teacher-made tests or educational test are constructed by the teachers based on the
contents pf different subjects taught.
Diagnostic tests are used to measure a student’s strengths and weaknesses, usually
to identify deficiencies in skills or performance.
Formative and Summative are terms often used with evaluation, but they may also
be used with testing. Formative testing is done to monitor students’ attainment of
the instructional objectives. Formative testing occurs over a period of time and
monitors student progress. Summative testing is done at the conclusion of
instruction and measures the extent to which students have attained the desired
outcomes

16. Standardized tests are already valid, reliable and objective.
Standardized tests are test for which contents have been selected
and for which norms or standards have been established.
Psychological test and government national examinations ate
examples of standardized tests.
Standards or norms are the goals to be achieved expressed in terms
of the average performance of the population tested. (265)

17. Criterion-referenced measure is a measuring device with a
predetermined level of success or standard on the part pf the test-
takers. For example, a level of 75 percent score in all the test items
could be considered a satisfactory performance.
Norm-referenced measure is a test that is scored on the basis of the
norm or standard level of accomplishment by the whole group taking
the test. The grades of the students are based on the normal curve of
distribution.

18. CRITERIA OF A GOOD EXAMINATION

19. Validity
-Refers to the degree to which a test measures what is intended to measure. It is the
usefulness of the test for a given measure.
-A valid test is always reliable. To test the validity of a test it is to be presented in
order to determine if it really measures what it intends to measure or what it
purports to measure.
Reliability
-Pertains to the degree to which a test measures what it supposed to measure.
-The test of reliability is the consistency of the results when it is administered to
different groups of individuals with similar characteristics in different places at
different times.
-Also, the results are almost similar when the test is given to the se group of
individuals at different days and the coefficient of correlation is not less than 0.85.

20. Objectivity
- Is the degree to which personal bias is eliminated in the scoring of
the answers? When refer to the quality of measurement, essentially,
we mean the amount of information contained in a score generated
by the measurement.
-Measures of student’s instructional outcomes are rarely as precise as
those pf physical characteristics such as height and weight.

21. -Students outcomes are more difficult to defined, and the units of measurements are
usually not physical units.
-The measures we take on students vary in quality, which prompts the need for
different scales of measurement. Terms that describe the levels of measurement in
these scales are nominal, ordinal, interval, ratio scales of measurement.
-The terms nominal, ordinal, interval, and ratio actually form a hierarchy.
-Nominal scales of measurement are the least sophisticated and contain the least
information.

22. -Ordinal, interval, and ratio scales increase respectively in
sophistication.
-The arrangement is a hierarchy in the higher levels, along with
additional data. For example, numbers from an interval scale of
measurement contain all of the information that nominal and ordinal
scales would provide, plus some supplementary input. However, a
ratio scale of the same attribute would contain even more
information than the interval scale. This idea will become clearer as
each scale of measurement is described.

23. -Are the least sophisticated; they merely classify objects or even by
assigning number to them.
-These numbers are arbitrary and imply no quantification, but the
categories must be mutually exclusive and exhaustive.
-For example, one could nominate designate baseball positions by assigning
the pitcher the numeral 1; the catcher, 2; the first baseman, 3; the second
baseman, 4; and so on. These assignments are arbitrary of these numbers
is meaningful. For example, 1 plus 2 does not equal 3, because a pitcher
plus a catcher does not equal a first baseman.
Nominal Measurement

24. -Ordinal scales classify, but they also assign rank order. An example of ordinal
measurement is ranking individuals in a class according to their test scores.
-Students’ scores could be ordered from first, second, third, and so forth to the
lowest score. Such a scale gives more information than nominal measurement,
but it still has limitations.
-The units of ordinal are most likely unequal. The number of points separating the
first and second students probably does not equal the number separating the
fifth and sixth students.
-These unequal units of measurement are analogous to a ruler in which some
inches are longer than others. Addition and subtraction of such units yield
meaningless number.
Ordinal Measurement

25. -In order to be able to add and subtract scores, we use interval scales,
sometimes called equal interval or equal unit measurement.
-This measurement scale contains the nominal and ordinal properties
and also characterized by equal units between score points.
-Examples include thermometers and calendar years.
Interval Measurement

26. -The most sophisticated type of measurement includes all the preceding
properties, but in a ratio scale, the zero point is not arbitrary; a score of zero
includes the absence of what is being measured.
-For example, if a person’s wealth equaled zero, he or she would have no wealth
at all. This is unlike a social studies test, where missing every item (i.e., receiving a
score of zero)
-Ratio measurement is rarely achieved in educational assessment, either cognitive
or affective areas.
Ratio Measurement

27. -When we contrast norm-referenced measurement (or testing) with
criterion-referenced measurement, we are basically refereeing to two
different ways of interpreting information. However, Popham (1988,
page 135) points out that certain characteristics tend to go with each
type of measurement, and it is unlikely that results of norm-
referenced test are interpreted in criterion-referenced ways and vice
versa.
Norm-Referenced and Criterion Referenced
Measurement

28. -The concepts of criterion-referenced testing have developed with a dual
meaning for criterion-referenced. On one hand, it means referencing an
individual’s performance to some criterion that is a defined performance
level. The individual’s score is interpreted in absolute rather than relative
terms. The criterion, in this situation, means some level of specified
performance that has been determined independently of how other might
perform.
-Second meaning of criterion-referenced involves the idea of a defined
behavioral domain – that is, a defined body of learner behaviors. The leaner’s
performance on a test is referenced to a specifically defined group of
behaviors. The criterion in this situation is the desired behaviors.
Criterion- Referenced Interpretation

29. Criterion – referenced interpretation is an absolute rather than relative
interpretation, referenced to a defined body of learner behaviors, or, as is
commonly done, to some specified level of performance.
-Criterion-referenced test require the specification of learner behaviors prior
to constructing the test. The behaviors should be readily identifiable from
instructional objectives. Criterion-referenced test tend to focus on specific
learner behaviors, and usually only a limited number are covered on any one
test.

30. Distinctions between Norm-Referenced and Criterion-
Referenced Tests

31. -Although interpretations, not characteristics, provide the distinction
between norm-referenced and criterion-referenced test, the two
types do tend to differ in some ways. Norm-referenced test are
usually more general and comprehensive and cover a large domain of
content and learning tasks. They are used for survey testing, although
this is not their exclusive use.

32. Test Length
- A major decision in the test planning is how many items should be included on
the test. There should be enough to cover the content adequately, but the length
of the class period or the attention span of fatigue limits of the students usually
restricts the test length. Decisions about test length are usually based on practical
constraints more than on theoretical considerations.
- Most teachers want test scores to be determined by how much the students
understands rather than by how quickly he or she answers the questions. Thus,
teachers prefer power items. Just how many items will fit into a given test
occasion is something that is learned through experience with similar groups of
students.

33. Item Formats
- Determining what kind of items is included on the test is a major decision.
Should they be objectively scored formats such as multiple choice or matching
type? Should they cause the students to organize their own thoughts through
short answer essay formats? These are important questions that can be answered
only by the teacher in terms of the local context, his or her students, his or her
classroom, and the specific purpose of the test. Once the planning decision is
made, the item writing begins. This tank is often the most feared by beginning
test constructors. However, the procedures are more common sense than formal
rules.

34. Norm-Referenced Interpretation
- Norm-referenced interpretation stems from the desire to differentiate among individuals or to
discriminate among the individuals for some defined group on whatever is being measured. In
norm-referenced measurement, an individual’s score in interpreted by comparing it to the scores
of a defined group, often called the normative group. Norms represents the scores earned by one
or more groups of students who have taken the test.
- Norm-referenced interpretation is a relative interpretation based on an individual’s position with
respect to some group, often called the normative group. Norms consist of the scores usually in
some form of descriptive statistics, of the normative group.
- In norm-referenced interpretation, the individual’s position in the normative group is of concern;
thus, this kind of positioning does not specify the performance in absolute terms. The norm being
used is the basis of comparison and their individual score is designated by the position in the
normative group.

35. - Suppose an algebra teacher has a total of 150 students in five classes, and the
classes have a common final examination. The teacher decides that the
distribution of letter grades assigned to the final examination performance will
be 10 percent. As 20 percent Bs, as percent Cs, 20 percent Ds, and 10 percent
Fs. (Note that the final examination grade as necessarily the course grade.)
Since that grading is based on all 150 scores, do not assess that 3 students in
each class will receive as, on the final examination.
- James receives a score on the final exam such that 21 students have a higher
score as 128 students have lower scores. What will James’s letter grade be on the
exam? The scores will receive as, and the next 30 scores (20 percent of 150) will
receive Bs classes from the top score down, James’s score is positioned 22nd, so
he will receive a B on the examination. Note that I this interpretation example, we
did not specify James’s actual

36. Achievement Test as an Example.
- Most standardized achievement tests, especially those covering several skills and
academic areas, are primarily designed for norm-referenced interpretations. However,
the form of results and the interpretations of these tests are somewhat complex and
require concepts not yet introduced in this text. Scores as teacher-constructed test are
often given norm-referenced interpretations. Grading on the curve, for example, is a
norm-referenced interpretation of test scores on some type of performance, measure.
Specified percentages of scores are assigned the different grades and an individual’s
score is positioned in the distribution of scores. (We mention this only as example; we do
not endorse this procedure).

37. POINTS TO BE CONSIDERED IN
PREPARING A TEST
1. Are the instructional objectives clearly defined?
2. What knowledge, skills and attitudes do want to measure?
3. Did you prepare a table of specifications?
4. Did you formulate well defined and clear test items?
5. Did you employ correct English in writing the items?
6. Did you avoid giving clues to the correct answer?
7. Did you test the important ideas rather than the trivial?
8. Did you adapt the test’s difficulty to your student’s ability?
9. Did you avoid using textbooks jargons?
10. Did you cast the items in positive forms?
11. Did you prepare a scoring key?
12. Does each item have single correct answer?
13. Did you review your items?

38. STAGES IN TEST CONSTRUCTION
I. Planning the Test
A. Determining the Objectives
B. Preparing the Table of Specifications
C. Selecting the Appropriate Item Format
D. Writing the Test Items
E. Editing the Test Items
II. Trying Out the Test
A. Administering the First Tryout- then Item Analysis
B. Administering the Second Tryout- then Item Analysis
C. Preparing the Final Form of the Test
III. Establishing Test Validity
IV. Establishing the Test Reliability
V. Interpreting the Test Score

39. MAJOR CONSIDERATIONS IN TEST
CONSTRUCTION
Type of Test
- Our usual idea of testing is an in-class test that is administered by the teacher. However,
there are many vibrations on this theme: group test, individual test, written test, oral test, speed
test, power test, pretest and post test. Each of these has different characteristics that must be
considered when the test is planned.
- If it is a take-home test rather than an in-class test, how do you make sure that students
work independently, have equal access to sources and resources, or speed a sufficient but not
enormous amount of time on the task? If it is a pretest, should it exactly match the past test so
that a gain score can be computed, or should the pretest contain items that are diagnostic of
prerequisite skills and knowledge? If it is an achievement test should partial credit be awarded,
should there be penalties for guessing, or should points be deducted for grammar and spelling
errors?
- Numerical score on the exam. That would have been necessary in order to determine
that his score position 22nd in the group of 150 scores. But in terms of the interpretation of the
score, it was based strictly on its position in the total group scores.

40. GENERAL PRINCIPLES IN CONSTRUCTING
DIFFERENT TYPES OF TEST
1. The test items should be selected very carefully. Only important facts should be included.
2. The test should have extensive sampling of items.
3. The test items should be carefully expressed in simple, clear, definite, and meaningful sentences.
4. There should be only one possible correct response for each test item.
5. Each item should be independent. Leading clues to other items should be avoided.
6. Lifting sentences from books should not be done to encourage thinking and understanding.
7. The first-person personal pronouns / and we should not be used.
8. Various types of test items should be made to avoid monotony.
9. Majority of the test items should be of moderate difficulty. Few difficult and few easy items should be
included.
10.The test items should be arranged in an ascending order of difficulty. Easy items should be at the beginning to
encourage the examinee to pursue the test and the most difficult items should be at the end.

41. 11. Clear concise and complete directions should precede all types of test. Sample test. Sample
test items may be provided for expected responses.
12. Items which can be answered by previous experience alone without knowledge of the subject
matter should not be included.
13. Catchy words should not be used in the test items.
14. Test items must be based upon the objectives of the course and upon the course content.
15. The test should measure the degree of achievement or determine the difficulties of the
learners.
16. The test should emphasize ability to apply and use facts as well as knowledge of facts.
17. The test should be of such length that it can be completed within the time allotted by all or
nearly all of the pupils. The teacher should perform the test herself to determine its approximate
time allotment.
18. Rules to governing good language expression, grammar, spelling, punctuation, and
capitalization should be observed in all times.
19. Information on how scoring will be done should be provided.

42. POINTERS TO BE OBSERVED IN
CONSTRUCTING AND SCORING THE
DIFFERENT TYPES OF TESTS
A. RECALL TYPES
1.Simple recall type
a) This type of consists of questions calling for a single word or expressions as an answer.
b)Items usually begin with who, where, when, and what.
c) Score is the number of correct answers.
2. Completion type
a. Only important words or phrases should be omitted to avoid confusion.
b. Blanks should be of equal lengths.
c. The blank, as much as possible, is placed near or at the end of the sentence.
d. Articles a, an, and they should not be provide before the end of omitted word or phrase to avoid clues for
answers.
e. Score is the number of correct answers.

43. 3. Enumeration Type
a. The exact number of expected answers should be started.
b. Blanks should be equal lengths.
c. Score is the number of correct answers.
4. Identification type
a. The items should make an examinee think of a word, number, or group of words that
would complete the statement or answer the problem.
b. Score is the number of correct answers.

44. B. RECOGNITION TYPES
1.True-false or alternate-response type
a. Declarative sentences should be used.
b. The number of “true” and “false” items should be more or less equal.
c. The truth or falsity of the sentence should not be too evident.
d. Negative statements should be avoided.
e. The “modified true – false” is more preferable than the plain true-false”.
f. In arranging the items, avoid the regular recurrence of “true” and “false” statements.
g. Avoid using specific determiners like: all, always, never, none, nothing, most, often, some, etc,
and avoid weak statements as may, sometimes, as a rule, in general etc.
h. Minimize the use of qualitative terms like; few, great, many, more, etc.
i. Avoid leading clues to answers in all times.
j. Score is the number of correct answers in “modified true-false and right answers minus wrong
answers in “plain true-false”.

45. 2.Yes-No type
a. The items should be in interrogative sentences.
b. The same rules as in true-false are applied.
3. Multiple-response type
a. There should be three to five choices. The number of choices used in the first item
should be the same number of choices in all the items of this type of test.
b. The choices should be numbered or lettered so that only the number or letter can be
written on blank provided.
c. If the choices are figures, they should be arranged in ascending order.
d. Avoid the use of “a” or “an” as the last word prior to the listing of the responses.
e. Random occurrence of responses should be employed
f. The choices, as much as possible, should be at the end of the statements.
g. The choices should be related in some way or should belong to the same class.
h. Avoid the use of “none of these” as one of the choices.
i. Score is the number of correct answers.

46. 4. Best answer type
a. There should be three to five choices all of which are
right but vary in their degree of merit, importance or
desirability
b. The other rules for multiple-response items are applied
here.
c. Score is the number of correct answers.

47. 5. Matching Type
a. There should be two columns. Under “A” are the stimuli which should be longer and
more descriptive than the responses under column “B”. The response may be a word, a phrase, a
number, or a formula.
b. The stimuli under column “A” should be numbered and the response under column “B”
should be lettered. Answers will be indicated by letters only on lines provided in column “A”.
c. The number of pairs usually should not exceed twenty items. Less than ten introduces
chance elements. Twenty pairs may be used but more than twenty is decidedly wasteful of time.
d. The number of responses in column “B” should be two or more than the number of
items in Column “A” to avoid guessing.
e. Only one correct matching for each item should be possible.
f. Matching sets should neither be to long nor too short.
g. All items should be on the same page to avoid turning of pages in the process of
matching pairs.
h. Score is the number of correct answers.

48. How to construct essay examinations.
1. Determine the objectives or essentials for each question to be
evaluated.
2. Phrase question in simple, clear and concise language.
3. Suit the length of the questions to the time available for
answering the essay examination. The teacher should try to answer
the test herself.
4. Scoring:
a. Have a model answer in advance.
b. Indicate the number of points for each question.
c. Score a point for each essential.

49. Advantages and Disadvantages of the
Objective Type of Tests
Advantages
a. The objectives test is free from personal bias in scoring.
b. It is easy to score. With a scoring key, the test can be corrected by
different individuals without affecting the accuracy of the grades given.
c. It has high validity because it is comprehensive with wide sampling of
essentials
d. It is less time-consuming since may items can be answered in a given time
e. It is fair to students since the slow writers can accomplish the test as fast
as writes.

50. Disadvantages
a. It is difficult to construct and requires more time to prepare.
b. It does not afford the students the opportunity in training for self-
and thought organization
c. It cannot be used to test ability in theme writing or journalistic
writing.

51. ADVANTAGES AND DISADVANTAGES
OF THE ESSAY TYPE OF TESTS
Advantages
a. The essay examination can be used in practically in all subjects of the school curriculum.
b. It trains students for thought organization and self-expression.
c. It affords students opportunities to express their originality and independence of thinking.
d. Only the essay test can be used in some subjects like composition writing and journalistic
writing in which cannot be tested by the objective type test.
e. Essay examination measures higher mental abilities like comparison, interpretation, criticism,
defense of opinion and decision.
f. The essay test is easily prepared.
g. It is inexpensive.

52. Disadvantages
a. The limited sampling of items makes the test unreliable measures of
achievements or abilities.
b. Questions usually are not well prepared.
c. Scoring is highly subjective due to the influence of the corrector’s personal
judgment.
d. Grading of the essay test is inaccurate measure of pupils’ achievements due to
subjective of scoring.

53. III. STATISTICAL MEASURES OR TOOLS
USED IN INTERPRETING NUMERICAL DATA
Frequency Distributions
- A simple, common sense technique for describing a set of test scores is through the use
of a frequency distribution. A frequency distribution is merely a listing of the possible score
values and the number of persons who achieved each score. Such an arrangement presents the
scores in a more simple and understandable manner than merely listing all of the separate
scores. Considers a specific set of scores to clarify these ideas.
- A set of scores for a group of 25 students who took a 50-items test is listed in Table 1. It is
easier to analyze the scores if they are arranged in a simple frequency distribution. (The
frequency distribution for the same set of scores is given in Table 2). The steps that are involved
in creating the frequency distribution are:
- First list the possible scores values in rank order, from highest to lowest. Then a second
column indicates the frequency or number of persons who received each score. For example,
three students received a score of 47, two received 40 and so forth. There is no need to list the
score values below the lowest score that anyone received.

56. - When there is a wide range of scores in a frequency distribution, the
distribution can be quite long, with a lot of zeros in the column of frequencies.
Such a frequency distribution can make interpretation of the scores difficult and
confusing. A grouped of frequency distribution would be more appropriate in
this kind of situation. Groups of score values are listed rather than each separate
possible score value.
- If we were to change the frequency distribution in Table 2 into a grouped
frequency distribution, we might choose intervals such as 48-50, 45-47, and so
forth. The frequency corresponding to interval 48-50 would be 9 (1+3+5). The
choice of the width of the interval is arbitrary, but it must be the same for all
intervals. In addition, it is a good idea to have as odd- numbered interval width
(we used 3 above) so that the midpoint of the interval is a whole number. This
strategy will simplify subsequent graphs and description of the data. The
grouped frequency distribution is presented in Table 3.

58. Frequency distributions summarize sets of test scores by listing the number of
people who received each test score. All of the test scores can be listed
separately, or the sources can be grouped in a frequency distribution.
MEASURES OF CENTRAL TENDEDNCY
- Frequency distributions are helpful for indicating the shape to describe a
distribution of scores, but we need more information than the shape to describe
a distribution adequately. We need to know where on the scale of measurement
a distribution is located and how the scores are dispersed in the distribution. For
the former, we compute measures of central tendency, and for the latter, we
compute measures of dispersion. Measures of central tendency are points on the
scale of measurement, and they are representative of how the scores tend to
average. There are three commonly used measures of central tendency; the
mean, the median, mode, but the mean is by far the most widely used.

59. The Mean
-The mean of a set of scores is the arithmetic mean. It is found by summing the
scores and dividing the sum by the number of scores. The mean is the most
commonly used measure of central tendency because it is easily understood and
is based on all of the scores in the set; hence, it summarizes a lot of information.
The formula for the mean is as follows:

61. The mean of the set of scores in Table 1 is 44.
The mean does not have to equal an observed
score; it is usually not even a whole number.

62. When the scores are arranged in a
frequency distribution, the formula is:
Where fX mdpt means that the midpoint of the interval is multiplied by the frequency for that
interval. In computing the mean for the scores in Table 3, using formula we obtain:
Note that this mean is slightly different than the mean using ungrouped data. This difference is
due to the midpoint representing the scores in the interval rather than using the actual scores.

63. The Median
- Another measure of central tendency is the median which is the point that divides the
distribution in half; that is, the half of the scores fall above the median and half of the scores fall
below the median.
- When there are only few scores, the median can often be found by inspection. If there is
an odd number of scores, the middle score is the median. Where there is an even number of
scores, the median is halfway between the two middles scores. However, when there are tied
scores in the middle’s distribution, or when the scores are in a frequency distribution, the
median may not be so obvious.
- Consider again the frequency distribution in Table 2. There were 25 scores in the
distribution, so the middle score should be the median. A straightforward way to find this median
is to augment the frequency distribution with a column of cumulative frequencies.
- Cumulative frequencies indicate the number of scores at or below each score. Table 4
indicates the cumulative frequencies for the data in Tale 2.

65. For example, 7 people scored at or below a score of 40, and 21
persons scored at or below a score of 48.
- To find the median, we need to locate the middle score in the
cumulative frequency column, because this score is the median.
Since there are 25 scores in the distribution, the middles one is the
13th, a score of 46. Thus, 46 is the median of this distribution; half of
the people scored above 46 and half scored.
- When there are ties in the middle of the distribution, there may
be a need to interpolate between scores to get the exact median.
However, such precisions are not needed for most classroom tests.
The whole number closest to the median is usually sufficient.

66. The Mode
- The measure of central tendency that is the easiest to find is the mode.
The mode is the most frequently occurring score in the distribution. The mode of
the scores in Table is 48. Five people had scores of 48 and no other score
occurred as often.
- Each of these three measures of central tendency – the mean, median,
and the mode means a legitimate definition of “average” performance on this
test. However, each does provide different information. The arithmetic average
was 44; half of the people scored at or below 46 and more people received 48
than any other score.
- There are some distributions in which all the three measures of central
tendency are equal, but more often than not they will be different. The choice of
which measure of central tendency is best will differ from situation to situation.
The mean is used most often, perhaps because it includes information from all of
the scores.

67. - When a distribution has a small number of very extreme scores, though,
the median may be a better definition of central tendency. The mode provides
the least information and is used infrequently as an “average”. The mode can be
used with nominal scale data, just as an indicator of the most frequently
appearing category. The mean, the median, and the mode all describe central
tendency:
The mean is the arithmetic average.
The median divides the distribution in half
The mode is the most frequent score.

68. MEASURES OF DISPERSION
- Measures of central tendency are useful for summarizing
average performance, but they tell as nothing about how the scores
are distributed or “spread out” but they might be differed in other
ways. One the distributions may have the scores tightly clustered
around the average, and the other distribution may have scores that
are widely separated. As you may have anticipated, there are
descriptive statistics that measures dispersion, which also are called
measures of variability. These measures indicate how spread out the
scores tends to be.

69. The Range
- The range indicates the difference between the highest and lowest scores
in the distribution. It is simple to calculate, but it provides limited information.
We subtract the lowest from the highest score and add 1 so that we include both
scores in the spread between them. For the scores of Tables 2, the range is 50 –
34 + 1 = 17.
- A problem with using the range is that only the two most extreme scores
are used in the computation. There is no indication of the spread of scores
between the highest and lowest. Measures of dispersion that take into
consideration every score in the distribution are the variance and the standard
deviation. The standard deviation is used a great deal in interpreting scores from
standardized test.

71. - The computation of the variance for the
scores of Tables 1 is illustrated in Table 5. The
data for students K through V are omitted to
save space, but these values are included in the
column totals and in the computation.

72. The Standard Deviation
The standard deviation also indicates how spread out the scores is, but it is expressed in
the same units as the original scores. The standards deviation is computed by finding the square
root of the variance.
S = S^2
For the data in Table 1, the variance is 22.8. The standard deviation is 22.8, or 4.77.
The scores of most norm groups have the shape of a “normal distribution-a symmetrical,
bell-shaped distribution with which most people are familiar. With normal distribution, about 95
percent of the scores are within two standard deviations of the mean.
Even when scores are not normally distributed, most of the scores will be within two
standard deviations of the mean. In the example, the mean minus two standard deviations is
34.46, and the mean plus two standard deviations is 53.54. Therefore, only one score is outside
of this interval; the lowest score, 43, is slightly more than two standard deviations from the
mean.

75. - The usefulness of the standard deviation becomes apparent when scores from different
test are compared. Suppose that two tests are given to the same class one fractions and the
other on reading comprehensive. The fractions test has a mean of 30 and a standard deviation of
8; the reading comprehensive test has a mean of 60 and a standard deviation of 10.
- If Ann scored 38 on the fractions test and 55 on the reading comprehensive test, it
appears from the raw scores that she did better in reading than in fractions, because 55 is
greater than 38.
- Descriptive statistics that indicate dispersion are the range, the variance, and the
standard deviation.
- The range is the difference between the highest and lowest scores in the distribution plus
one.
- The standard deviation is a unit of measurement that shows by how much the separate
scores tend to differ from the mean.
- The variance is the square of the standard deviation. Most scores are within two
standard deviations from the mean.

76. Graphing Distributions
A graph of a distribution of test scores is often better understood than is the frequency
distribution or a mere table of numbers.
-The general pattern of scores, as well as any unique characteristics of the distribution, can be
seen easily in simple graphs. There are several kinds of graph that can be used, but a simple bar
graph or histogram, is as useful as any.
The general shape of the distribution is clear from the graph. Most of the scores in this
distribution are high, at the upper end of the graph.
-Such a shape is quite common for the scores of classroom tests.
-A normal distribution has most of the test scores in the middle of the distribution and
progressively fewer scores toward extremes. The scores of norm groups ate seldom graphed but
they could be if we were concerned about seeing the specific shape of the distribution of scores.

77. ASSESSMENT OF LEARNING