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1.0 Introduction

As a student of B.Ed. (Hons) at
Institute of Education and Research, I went through a course named Practicum
where I have completed a three and a half month internship as trainee teacher
at Engineering University Girls School. I took two classes each day- Social
Science of class Six (B) and Social Science of class Eight (A).During my role
as a teacher I executed some tests for both the classes to determine the
pupils’ common trend, their individual strengths and weaknesses and to give
feedback and to fulfill my practicum requirements as well. However in this
report my objective is not to picture through pupils individual trends as my
course doesn’t require it(although T – scores determined in this report show
students’ relative individual position ), rather I shall try to analysis the
tests I have taken, test results, comparison of test results and make comment
over the general trend of the class, not specific. I shall briefly compare
between the results of 1st semester and 2nd semester social science examination
of the respective classes in order to determine if my teaching could be able to
bring more improvement of the pupil (I taught between the period of 1^st
and 2^nd semester exam.) and if the school teachers’ comment about
their pupil is right or wrong (they think their students are very much dull-not
meritorious at all and their improvement is very difficult because of their
poor social and economic background). Moreover I have an intention to make some
suggestion at ending remark to improve the existing assessment system of Engineering
University Girls School.

This report includes only the
analysis of class Six’s test and test results.

2.0 Review of related literature

2.1 Statistical Analysis

Statistical analysis of particular
test or test result includes the collection, presentation, and analysis of the
scores and a significant explanation as well as decision from that analysis.
Statistical analysis includes some specific and systematic steps, methods and
measurement.

2.2
Item Specification Table

Item specification table is used to
determine the degree of pupils’ achieved desirable behavioral change. It is
prepared before the execution of evaluation activity basing on the importance
of content and learning objectives in terms of behavioral domains. This work
plan is done in order to prepare items of the test.

2.3
Reliability of test

A test is called reliable when its
scores are stable and trustworthy.

s²}]

n
= Number of items of the test

M
= Arithmetic mean of the scores

s =
Standard deviation

2.4 Frequency Distribution

Frequency distribution helps to
classify or sort ungrouped data in a systematic way according to the frequency.
It enables the researcher to make the data meaningful.

2.5 Range

Range is the difference between the
highest and the lowest scores.

2.6 Class Interval

The scores have to be arranged in
some small groups. The distance or difference of such a class is called class
interval.

# Number of the class = (Range/class Interval) +1

2.7 Tabulation of scores

This is done in two steps. The first
one is totally the scores in their proper intervals and the second one is to
count the tallies and find out the frequency of each class interval. The sum of
the frequencies is called N.

2.8 Mid Point of the Class Interval

# Mid Point = Lower limit of the class+(upper
limit of the class -lower limit of the class)/2

2.9 Measures of Central Tendency

Measures of central tendency give the
researcher a convenient if describing a set of data with a single number. The
number resulting from computation of a measure of central tendency represents
the average or typical score attained by a group of subjects. Measures of
central tendencies are:

2.9.1 Mean

The mean is the arithmetic average of
the scores and is the most frequently used measure of central tendency.

# True Mean = A.M.+(Σfd/N)i

A.M.=
Assumed Mean

f
= Frequency

d
= Deviation from the class Interval containing Assumed Mean

Σfd
= Summation of the products of f and d

N
= Total frequency

i
= Interval length

2.9.2 Median

The median is that point in a
distribution above and below which are 50% of the scores; in other words, the
median is the midpoint.

# Median = L+{(N/2-cfu)/fm}i

L
= Lower point of the median class

Cfu
= Cumulative frequency of the class below the median class

fm
= Frequency of the median class

i
= Interval length

N
= Total frequency

2.9.3 Mode

The mode is
the score that is attained by more subjects than any other score.

# Mode = 3 median – 2 mean

2.10 Measures of
Variability

Measures of central tendency have some limitations. Even an
ideal average can represent a series only as best as a figure can. Measures of
central tendency fail to reveal the entire story of the phenomenon.

2.10.1 Range

The range is simply the difference between the highest and
lowest score in a distribution and is determined by subtraction.

# Range = Highest score – Lowest score

2.10.2 Quartile Deviation

The
quartile deviation is one half of the difference between the upper quartile
(the 75^th percentile) and lower quartile (the 25^th
percentile) in a distribution.

# Q = ( Q₃– Q₁)/2

Q
= Quartile deviation

Q₃
= 75^th percentile

Q₁= 25^th percentile

# Q₁ = L₁ +
{(N/4-F₁)/fq₁}i

L₁
= Lower point of the 25^th percentile class interval

F₁
= Cumulative frequency of the class below the 25^th Percentile
class

fq₁
= frequency of the class interval of 25^th percentile

i
= Length of the class interval

N = Total frequency

# Q₃ = L₃ +
{(3N/4 – F₃)/fq₃}i

L₃
= Lower point of the 75^th percentile class interval

F₃
= Cumulative frequency of the class below the 75^th Percentile
class

fq₃
= frequency of the class interval of 75^th percentile

i
= Length of the class interval

N = Total frequency

2.10.3 Mean Deviation

Mean deviation (M.D.) is
the arithmetic make of all the scores in a series taken from their mean,
occasionally from the mode or median.

S||
/N

D
= Distance between the midpoint of the
class and the mean

f
= Frequency of that class

N
= Sum of the frequencies

2.10.4 Standard Deviation

The standard deviation is the
most stable measure of variability and takes in account each and every score.
It differs from M.D. in several aspects such as:

In computing M.D., we
disregard signs, whereas in finding S.D., we avoid the difficulty of signs by
squaring the separate deviation.

The squared deviation used
in computing S.D. is always taken from the mean.

s
= ÖSfd²/N
– (Sfd/N)²}i

D
= Deviation

F
= frequency

i
= Length of the class interval

N = Total frequency

2.11 Measures of relative position

Measures of relative position
indicate when a score is in relation to all other scores in a distribution. A
major advantage of such measures is that they make it possible to compare the
performance of an individual in two or more different tests. Major measures of
relative position are:

2.11.1 Percentile Ranks

A percentile rank indicates the percentage of scores that
fall at or below a given score. It shows the comparative position of a student
in a class.

# Percentile Rank (P.R) = {f_c
+ (X-L)/ i x q} 100/N

f_c = Cumulative frequency of the classes
below the class of that particular class

X = The score of which the P.R has to be determined

L = Lower limit of the class which contains that
particular score

i = Length of the class interval

q = The frequency of that class

N = Total frequency

2.11.2 Standard score( Z – Score )

# Standard score (Z – Score), Z
= (X – M) / s

X = Score of the student

M = Mean score of the class

s2.11.3 Standard score (T – Score)

A T – Score is nothing more than a Z
– Score expressed in a different form.

2.12 Measures of relationship

Degree of relationship is expressed as a correlation
coefficient, which is computed, based on the two sets of scores. If the change
in one set of score causes the change of the other set of score, then this
phenomenon is called the correlation. The most appropriate measure of
correlation is :

N
SSSY

¡ =

ÖSX²
– ( SX )² }{ NSSY )²
}

X = Score of test 1

Y = Score of test 2

N = Total frequency

2.13 Measures of relationship

Degree of relationship is expressed
as a correlation coefficient, which is computed, based on the two sets of
scores. If the change in one set of score causes the change of the other set of
score, then this phenomenon is called the correlation. The most appropriate
measure of correlation is :

N
SSSY

¡ =

ÖSX² – ( SX )² }{ NSY² – ( SY )² }

X = Score of test 1

Y = Score of test 2

N = Total frequency

2.14 Normal Distribution and Normal
Probability Curve

If a variable is normally
distributed, that is, does for a normal curve, and then several things are
true:

50% of the scores are above the mean and 50% are below
the mean.
The mean, the median, and the mode are the same.
Most scores are near the mean and the further from the
mean a score is, the fewer the number of subject who attained that score.

·
·
·
·

· Mean – 3.0 S.D = Approximately the
0.1 Percentile

· Mean – 2.0 S.D = Approximately the 2^nd
Percentile

· Mean – 1.0 S.D = Approximately the 16^th
Percentile

· Mean = Approximately the 50^th
Percentile

· Mean + 1.0 S.D = Approximately the 84^th
Percentile

· Mean + 2.0 S.D = Approximately the 98^th
Percentile

· Mean + 3.0 S.D = Approximately the 99⁺
Percentile

0.13%

2.15%

13.59%

34.13%

13.59%

2.15%

0.13%

sss
Mean 1 sss

Fig: The normal probability curve

2.15 Abnormal Distribution
2.15.1 Skewness

# Skewness = 3 ( mean – median ) /
S.D

2.15.2 Kurtosis

Kurtosis indicates to what degree a
distribution is pointed or flat in comparison to normal probability curve. It
can be of three types:

2.15.2.1 Leptokurtic

It is more pointed than the normal
curve.

2.15.2.2
Platykurtic

It is more flat than a normal curve.

2.15.2.3 Mesokurtic

If the curve is neither too much
pointed, nor too much flat, then the curve is mesokurtic or normal.

2.16 Grading System

The grading system is based on
integration of the traditional absolute marking system and grading student
performance assuming normal distribution. The system is a two tier evaluation
system, which will ensure gradation of the group as a whole in a course, and
that of individuals which the group in comparison with one another.

3.0 General considerations

In preparing the essay type test,
understated matters have been tried to maintain:

i.
1.
It is a 15-mark test. Total item no. is 6.

ii.
The
duration of the test is 30 minutes. Time per mark is 2 minutes.

iii.
The
test has been constructed mainly with short essay type questions rather than
broad essays in order cover more areas of the content.

iv.
Short
essays enabled the increase of items in number in order to cover more areas of
content.

v.
Overlapping
of content between the essay type and MCQ type questions has been avoided.

vi.
Effort
is made to use proper language so that the pupils can easily understand the
requirements of the test. Simple to complex sequence was tried to maintain.

vii.
Mix
up of other type of questions with the essay type test has been avoided.

viii.
Optional
questions are not given.

ix.
Item
and sub-item wise number distribution was shown in the test and key words were
underlined so that the students can prepare their answers according to the
number distribution.

3.0.1Test and Examination –
Explanation of the situation

To fulfill my practicum requirement, I had to execute a
50-mark essay type test and a 50 mark MCQ test. But school authority did
not allow me to take a two-hour or of more duration test. So I had to take
the 50-mark essay type test in 4 parts:

Essay Type Test

Class Test no	Date	Major Subject	Syllabus	Duration	Total Marks
1	19/05/09	Economics	Two fundamentals of Economics, Economic activities of human being	35 Min	10
2	27/05/09	Geography	The Asia continent	40 Min	05
3	03/06/09	The Gupta dynasty in Indian sub-continent, The Gupta and Mourjo dynasty in Bengal, Bangladesh in ancient period and ancient settlements in Bengal	35 Min	08
4	08/07/09	Sociology	Evolution of human society-stone age and ancient society	40 Min	07
				150 Min	30

QUESTION
-1

4.1.1 Analysis of Test-1

4.1.1.2 Subject wise
Distribution

Integrated Social Science has been
designed including major six subjects:

Sociology
History
Geography
Political Science
Economics
Population Education

But
Political Science and Population Education were not included for 2^nd
semester. So, I had to teach and take tests without those subjects.

The essay type test has included all
other subjects. Subject wise number distribution is shown below:

Subject	Subject range	Distributed Marks	Percentage (%)
Sociology	7 pages	12	24
History	8 pages	12	24
Geography	9 pages	14	28
Economics	7 pages	12	24
	31 pages	50	100

Comment

Distribution of marks differed
because of the difference of ranges among the subjects. This table clearly
shows that an overall equivalency of number distribution according to the
subject range has been tried to maintain in sociology, geography, history and
economics Number per page is 1.61 (approx). According to page range if 100%
equivalency of number distribution is to be maintained, then for sociology
(7×1.61)=11.27, for history (8×1.61)=12.88, for geography (9×1.61)=14.49,for
economics (7×1.61)=11.27, number is to be required to distribute. This figure
is not too far from the real distributed mark.

4.1.1.3 Item
Specification

The item specification according
to the domains of objectives of the essay type test is shown below:

Objective	Knowledge		Comprehension		Application		Analysis		Synthesis		Evaluation		Total mark
Percentage	32%		20%		22%		8%		10%		8%
	Mark	No. of item	Mark	No. of item	Mark	No. of item	Mark	No. of item	Mark	No. of item	Mark	No. of item
Sociology	0	0	4	1	0	0	4	1	0	0	4	1	10
History	7	3	0	0	0	0	0	0	5	1	0	0	05
Geography	6	2	2	1	6	1	0	0	0	0	0	0	08
Economics	3	1	4	2	5	2	0	0	0	0	0	0	07
Total	16/6		10/4		11/3		4/1		5/1		4/1		30

Comment

Measure of difficulty level and
discrimination power is appropriate for MCQ or objective type tests; not for
essay type test. So these two parameters is not measured here for the essay
type test.

A good test requires validity,
reliability and objectivity. Objectivity can’t be statistically determined. I
don’t have sufficient data to measure the validity of the test. Reliability can
be measured following the ‘Kuder and Richardson Method’. The reliability of the
test is determined below:

4.1.1.4 Reliability

#
Reliability, r₁=
n/(n-1)[1-{M(n-M)/ns²}]

n = 16

M = 17.9 (Determined later on)

s^{= 6.2 (Determined later on)}

s² } ]
= 1.13 (Apprx.)

Subject
wise comparative number distribution

Domain wise comparative number
distribution

QUESTION-2

4.2.1.2 General considerations

In
preparing the Multiple Choice Questions (MCQ), understated matters have been
tried to maintain:

1.
It is a 50-mark test. Total item no. is 50.Mark
per item is 1. The duration of the test is 30 minutes. Time for each item is 36
seconds. Students were required to give tick mark (√) on the correct answer.50
minutes is not given as it was not a circle fill up test. So less time was
required. All 36 seconds could be used for thinking.

Four distractors are given for each item. Only one is
correct answer.
To make guessing difficult, distractors of a specific
item are similar in length; no specific distractor is too lengthy than
others, nor it is too short.
The correct answers are arranged in a way so that
students can’t guess it from the arrangement. For example: among 50 items,
a total of 14 correct answers was arranged in distractor (Ka), 13 from distractor (kha), 12 from
distractor (Ga),11 from distractor
(Gha). And the correct answers is not arranged serially, rather it is
random. So it was difficult to answer correctly basing on guess.
Distractors of a specific item are plausible and
homogeneous, not heterogeneous automatically eliminated.
‘All of the above’, ‘None of the above’-this type of
distractors is not given. These distractors weaken the test.
Negative sense distractors have been avoided.
Stems and distractors have been clearly written so that
it could make clear sense and avoid misconception.
Unfamiliar words are not used.Key words were underlined
to give clear concept.
Irrelevant clue is not given in the stem or distractors.
Overlapping distractors is not given.Simple to complex
sequence was tried to follow.
MCQ is prepared mainly from that area of the content,
which was not included in the essay type test. So, combined essay type and
MCQ test together has covered a large area of the content to assess
pupils’ overall performance of the subject.

4.2.1.3 Subject wise Distribution

The MCQ test has included all the
subjects. Subjectwise number distribution is shown below:

Subject	Subject range	Distributed Marks	Percentage (%)
Sociology	7 pages	10	24
History	8 pages	07	24
Geography	9 pages	08	28
Economics	7 pages	05	24
	31 pages	30	100

Comment

Distribution of marks differed
because of the difference of ranges among the subjects. This table clearly
shows that an overall equivalency of number distribution according to the
subject range has been tried to maintain. Number per page is 1.61 (approx).
According to page range if 100% equivalency of number distribution is to be
maintained, then for sociology (7×1.61)=11.27, for history (8×1.61)=12.88, for
geography (9×1.61)=14.49, for economics (7×1.61)=11.27 number is to be required
to distribute. This figure is not too far from the real distributed mark. So
the distribution of numbers is generally equivalent.

4.2.1.4 Item
Specification

The item specification according
to the domains of objectives of the MCQ test is shown below:

Objective	Knowledge		Comprehension		Application		Analysis		Synthesis		Evaluation		Total mark
Percentage	68%		6%		8%		4%		4%		10%
	Mark	No. of item	Mark	No. of item	Mark	No. of item	Mark	No. of item	Mark	No. of item	Mark	No. of item
Sociology	9	9	1	1	0	0	0	0	1	1	1	1	10
History	10	10	0	0	0	0	0	0	0	0	2	2	07
Geography	13	13	1	1	0	0	0	0	0	0	0	0	08
Economics	2	2	1	1	4	4	2	2	1	1	2	2	05
Total	34/34		3/3		4/4		2/2		2/2		5/5		30

Comment

A good test covers all the domains of
learning such as knowledge, comprehension, application, analysis, synthesis,
and evaluation. This test fulfills this requirement covering all the domains of
learning. A test should not be too easy or too difficult. In this regard, 68%
items has been given from knowledge sub-domain; items have also been taken from
higher sub-domains such synthesis, evaluation, etc. It has been done in order
to make the test neither too easy nor too difficult and to cover all learning
domains as well. But the test has a limitation. Usually the higher level of
domain is lower the mark is distributed for the domain. This test couldn’t
follow this rule properly. For example: 3 marks has been distributed for
comprehension sub-domain, wheras 5 mark was given to assess evaluation power.
This irrelevancy can also be observed in application sub-domain. Another
limitation is each subject area couldn’t cover every domains of learning. As a
test maker I feel this quite difficult to prepare an MCQ test covering all the
criterias. This can make the test too much difficult, especially for the
students who have always faced
traditional knowledge based tests and increase their exam fearness.
Fully standardized test can be applied to them step-by-step and only after
providing proper learning situations.

4.2.1.5 Determining Difficulty level

A test is prepared considering
whether it should not be to easy or too difficult, a certain group of pupils
may feel it normal or too difficult or too easy according to their merit level,
learning experience, test experience, social and economic background, etc. As a
teacher I tried to make a not too easy not too difficult test and designed my
teaching-learning activities relevant to the objectives and test. But the
students may feel different about the test because of their pre-mentioned
criteria. So it is necessary to determine if the pupil feel the items are too
difficult or too easy. In this manner determining difficulty level and
discrimination power of the items are necessary.

# Difficulty Level, D = (R/N) 100

R = H + L

R = Number of pupils who answered
the item correctly.

H = Number of pupils of high score
group who answered the item correctly( Upper 27% ).

L = Number of pupils of low score
group who answered the item correctly(Lower 27% ).

N = Total number of pupils who
tried the item.

58 students attended the MCQ test.
Out of 58, upper 27% is upper 15.66 students and lower 27% is lower 15.66
students. I shall count the scores of upper 16 students and lower 16 students.
So here:

H = Number of pupils of high score
group(Upper 16) who answered the item correctly.

L = Number of pupils of low score
group(Lower 16) who answered the item correctly.

N = 16 +16 = 32, if all the
students of both upper and lower group try the item.

The item wise value of H, L and N
will be directly counted in the table below; not separately shown here.

Serial no of Item	Manipulation of Data According to formula	Determined difficulty level
1	{(9 + 3) / 32 } x 100	37.5%
2	{(7 + 8) / 32 } x 100	46.9%
3	{(4 + 6) / 32 } x 100	31.3%
4	{(13 + 11) / 32 } x 100	75.0%
5	{(8 + 6) / 32 } x 100	43.8%
6	{(9 + 6) / 32 } x 100	46.9%
7	{(13 + 9) / 32 } x 100	68.8%
8	{(16 + 12) / 32 } x 100	87.5%
9	{( 8 + 3) / 32 } x 100	34.3%
10	{( 8 + 5) / 32 } x 100	40.6%
11	{(14 + 8) / 32 } x 100	68.8%
12	{(6 + 4) / 32 } x 100	31.3%
13	{(5 + 4) / 32 } x 100	28.1%
14	{(10 + 6) / 32 } x 100	50.0%
15	{(6 + 2) / 32 } x 100	25.0%
16	{(12 + 9) / 32 } x 100	65.6%
17	{(9 + 9) / 32 } x 100	56.3%
18	{(6 + 2) / 32 } x 100	25.0%
19	{(16 + 10) / 32 } x 100	81.3%
20	{(7 + 5) / 32 } x 100	37.5%
21	{(7 + 4) / 32 } x 100	34.3%
22	{(16 + 9) / 32 } x 100	78.1%
23	{(8 + 7) / 32 } x 100	46.9%
24	{(6 + 6) / 32 } x 100	37.5%
25	{(16 + 16) / 32 } x 100	1.0%
26	{(16 + 14) / 32 } x 100	93.8%
27	{(12 + 8) / 32 } x 100	62.5%
28	{(10 + 6) / 32 } x 100	50.0%
29	{(16 + 13) / 32 } x 100	90.6%
30	{(12 + 6) / 32 } x 100	87.5%
31	{(5 + 4) / 32 } x 100	28.1%
32	{(11 + 10) / 32 } x 100	65.6%
33	{(16 + 8) / 32 } x 100	75.0%
34	{(10 + 7) / 32 } x 100	53.1%
35	{(15 + 5) / 32 } x 100	62.5%
36	{(10 + 3) / 32 } x 100	40.6%
37	{(10 + 5) / 32 } x 100	46.8%
38	{(7 + 9) / 32 } x 100	50.0%
39	{(15 + 8) / 32 } x 100	71.8%
40	{(5 + 3) / 32 } x 100	25.0%
41	{(6 + 4) / 32 } x 100	31.3%
42	{(4 + 5) / 32 } x 100	28.1%
43	{(6 + 3) / 32 } x 100	28.1%
44	{(15 + 9) / 32 } x 100	75.0%
45	{(7 + 2) / 32 } x 100	28.1%
46	{(9 + 6) / 32 } x 100	46.8%
47	{(9 + 3) / 32 } x 100	37.5%
48	{(9 + 6) / 32 } x 100	46.8%
49	{(9 + 7) / 32 } x 100	50.0%
50	{(9 + 4) / 32 } x 100	40.6%

Comment

A good MCQ test contains more items
of difficulty level near 50.A table is given below to show the no. of items the
according to their difficulty level range:

Range of Difficulty Level	Number of items
0-10	0
11-20	1
21-30	8
31-40	9
41-50	12
51-60	3
61-70	6
71-80	5
81-90	3
91-100	3
0-100	50

It is clearly seen that there are 34
items between 0.30-0.70 difficulty levels, 15 items between 41-60 difficulty
levels. So the test has generally followed the rule of difficulty level.

4.2.1.6 Discriminating Power

# Discriminating Power, D.P = (H – L)
/ (N/2)

H = No. of correct responses from
the upper 16

L = No. of correct responses from
the lower 16

N = Total number of pupils who
tried the item = 16 + 16= 32; N/2 = 32/2 = 16

Serial no of Item	Manipulation of Data According to formula	Determined Discriminating Power
1	(9 – 3) / 16	+0.38
2	(7 – 8) / 16	-0.06
3	(4 – 6) / 16	-0.13
4	(13 – 11) / 16	+0.13
5	(8 – 6) / 16	+0.13
6	(9 – 6) / 16	+0.19
7	(13 – 9) / 16	+0.25
8	(16 – 12) / 16	+0.25
9	(8 – 3) / 16	+0.31
10	(8 – 5) / 16	+0.19
11	(14 – 8) / 16	+0.38
12	(6 – 4) / 16	+0.13
13	(5 – 4) / 16	+0.06
14	(10 – 6) / 16	+0.25
15	(6 – 2) / 16	+0.25
16	(12 – 9) / 16	+0.19
17	(9 – 9) / 16	0
18	(6 – 2) / 16	+0.25
19	(16 – 10) / 16	+0.38
20	(7 – 5) / 16	+0.13
21	(7 – 4) / 16	+0.19
22	(16 – 9) / 16	+0.43
23	(8 – 7) / 16	+0.06
24	(6 – 6) / 16	0
25	(16 – 16) / 16	0
26	(16 – 14) / 16	+0.13
27	(12 – 8) / 16	+0.25
28	(10 – 6) / 16	+0.25
29	(16 – 13) / 16	+0.19
30	(12 – 6) / 16	+0.38
31	(5 – 4) / 16	+0.06
32	(11 – 10) / 16	+0.06
33	(16 –8) / 16	+0.50
34	(10 – 7) / 16	+0.19
35	(15 – 5) / 16	+0.63
36	(10 – 3) / 16	+0.43
37	(10 – 5) / 16	+0.31
38	(7 – 9) / 16	-0.13
39	(15 – 8) / 16	+0.43
40	(5 – 3) / 16	+0.13
41	(6 – 4) / 16	+0.13
42	(4 – 5) / 16	-0.06
43	(6 – 3) / 16	+0.19
44	(15 – 9) / 16	+0.25
45	(7 – 2) / 16	+0.31
46	(9 – 6) / 16	+0.19
47	(9 – 3) / 16	+0.38
48	(9 – 6) / 16	+0.19
49	(9 – 7) / 16	+0.13
50	(9 – 4) / 16	+0.31

Comment

Items containing discrimination power
of +o.40 and above are considered very good item, items in between +0.20 to
+0.40 is considered satisfactory item, between 0 to 0.20 is considered weak
item and item having negative value is considered very weak item. A table is
given below to show the no. of items according to their discrimination power:

Range of D.P.	Number of items	Comment
+0.40 and above	5	Very good item
+0.19 to +0.39	26	Satisfactory item
0 to +0.19	15	Weak item
D.P. of negative value	4	Very weak item

It is to be noted that as many item
has a discriminating power of +0.19,this score has been included as
satisfactory item(it is very near to +.20).31 items of the test is either very
good or satisfactory item, which is 62% of the total items. That is a good
sign. But a good test should avoid items of negative values.4 items of the test
are of negative values. That is a limitation of the test.

A good test requires validity,
reliability and objectivity. As it is an MCQ test, it must be objective. I
don’t have sufficient data to measure the validity of the test. Reliability can
be measured following the ‘Kuder and Richardson Method’. The reliability of the
test is determined below:

4.2.1.7
Reliability

# Reliability, r₁=
n/(n-1)[1-{M(n-M)/ns^}]

n = 50

M = 22.75 ( Determined later on )

s^{= 3.65 ( Determined later on )}

r₁= n / (n-1) [ 1 – {
M(n-M) / ns²} ] = 0.08 (Apprx)

Reliability =0.08 (Apprx) ;
Test’s Reliability is low

4.2.1.8 Graphic presentation of Test – 2 analysis

Subject wise
comparative number distribution

Domain wise comparative number
distribution

Number of items according to
Difficulty Level

Sorting of items according to
Discriminating Power

4.3 Graphic comparison between Test-1
and test-2

Subject wise comparative number
distribution

Comparison between Reliability

Comment

Subject wise comparative number
distribution between Test-1 and Test-2 is exactly similar. Domain wise
comparative number distribution between Test-1 & Test-2 is not similar.
Distribution of marks largely differs in knowledge, comprehension, application
and synthesis sub-domains. Reliability of Test-1 is higher than that of Test
–2. Usually descriptive essay type test doesn’t require item analysis. So it is
not done here.

5.0 Test Result Analysis

5.1 Analysis of Test-1 results

Student’s score in Test-1

Total student number of the class is
67.Here, to make a decent analysis and comparison, only the scores of the
students were given who attended both essay type and MCQ test.

Roll No.	Obtained Mark (out of 30)	Roll No.	Obtained Mark (out of 30)
01	27	20	17.5
02	22	21	18
03	16.5	22	11.5
04	19	23	10
05	11	24	19.5
06	16	25	Absent
07	25	26	18
08	23	27	13
09	14	28	20
10	21	29	Absent
11	09	30	19
12	19	31	12
13	21.5	32	12
14	Absent	33	18
15	11	34	18
16	26.5	35	15
17	12.5	36	23
18	22	37	19
19	9	38	23.5
39	22	43	11.5
40	15	44	22
41	26	45	28.5
42	12.5

Tabulation of scores

# Number of the class = (Range/class Interval) +1

= 4.5 + 1

= 5.5

Frequency Distribution Table

Class Interval (C.I.)	Tallies	Frequency
6 – 10	7
11 – 15	\|\|\|\| \|\|\|\| \|\|\|\|	15
16 – 20	\|\|\|\| \|\|\|\| \|\|\|\| \|	16
21 – 25	\|\|\|\| \|\|\|\| \|\|\|	13
26 – 30	\|\|\|\| \|	6
31 – 35	\|	1

N = 58

5.1.1 Measures of Central Tendency

5.1.1.1 The Mean

# True Mean = A.M.+(Σfd/N)i

C.I.

Mid point

Frequency (f)

Deviation (d)

Product (fd)

6 – 10

– 2

– 14

11 – 15

– 1

– 15

16 – 20

21 – 25

+ 1

+ 13

26 – 30

+ 2

+ 12

31 – 35

+ 3

Σfd = – 1

Here –

A.M. = 18

Σfd = – 1

N = 58

True Mean = A.M.+(Σfd/N)i

= 18 + (- 1/58) 5

Mean = 17.9

5.1.1.2 The Median

# Median = L+{(N/2-cfu)/fm}i

C.I.	Lower and upper limit of C.I.	Frequency (f)	Cumulative Frequency (cfu)
6 – 10	5.5 – 10.5	7	7
11 – 15	10.5 – 15.5	15	22
16 – 20	15.5 – 20.5	16	38
21 – 25	20.5 – 25.5	13	51
26 – 30	25.5 – 30.5	6	57
31 – 35	30.5 – 35.5	1	58

Here-

L = 15.5

Cfu = 22

fm = 16

i = 5

N = 58

= 15.5 + {(29 – 22)/16} 5

Median = 17.7

5.1.1.3
The Mode

Mode = 3 median – 2 mean

Mode = 17.3

Comment

The value of mean, median and
mode is respectively 17.9, 17.7 and 17.3.The value of mean, median and mode is nearer to each other..
Here 15 – 20 class interval contains maximum number of frequency and mean,
median and mode belong to that class interval.11 – 15, 16 – 20 and 21 – 25
class intervals contain a total of 44 scores together, that is 75.9% of the
total score. It shows that the scores have very high central tendency.

5.1.2 Measures of Variability

5.1.2.1 The Range

Range = 22.5

5.1.2.2 The Quartile Deviation

# Q₁ = L₁ + {(N/4-F₁)/fq₁}I

Here-

L₁
= 15.5

F₁
= 22

fq₁
= 16

i
= 5

N = 58

Q₁ = L₁ +
{(N/4-F₁)/fq₁} i

= 15.5
+{(14.25 – 22)/16} 5

= 15.5 + {(- 7.25)/23} 5

= 15.5 + (-0.32) 5

= 15.5 – 1.6

=
13.9

Q₁= 13.9 (Apprx.)

# Q₃ = L₃ + {(3N/4 – F₃)/fq₃}
i

Here-

L₃ = 20.5

fq₃ = 13

N = 58

Q₃ = L₃ + {(3N/4
– F₃)/fq₃} I

=
20.5 + (0.44) 5

=
20.5 + 2.22

=
22.72

Q₃ = 22.72 (Apprx.)

Quartile Deviation, Q = ( Q₃–
Q₁)/2

= (22.72 – 13.9)/2

= 8.82/2

= 4.41

Quartile
Deviation = 4.41 (Apprx.)

5.1.2.3
Mean Deviation

S||
/N

C.I.	Mid point (X)	Mean	f	d = x – M	fd
6 – 10	8	17.9	7	– 9.9	– 69.3
11 – 15	13	17.9	15	– 4.9	– 73.5
16 – 20	18	17.9	16	– 0.1	– 1.6
21 – 25	23	17.9	13	+ 5.1	+ 66.3
26 – 30	28	17.9	6	+ 10.1	+ 60.6
31 – 35	33	17.9	1	+ 15.1	+ 15.1

S||
= 286.4

Here-

S|fd| = 286.4

N = 58

S||
/N

=
286.4/58

= 4.94

Mean Deviation = 4.94 (Apprx.)

5.1.2.4 Standard Deviation

s
= ÖSfd²/N
– (Sfd/N)²}I

C.I.	f	Deviation (d)	fd	fd²
6 – 10	7	– 2	– 14	28
11 – 15	15	– 1	– 15	15
16 – 20	16	0	0	0
21 – 25	13	+ 1	+ 13	13
26 – 30	6	+ 2	+ 12	24
31 – 35	1	+ 3	9

∑fd = – 1
∑fd²=89

∑fd = – 1

∑fd²= 89

i =5

N = 58

sÖSSfd/N)²}i

Ö{89/58 –
(- 1/58)²} x 5

Ö{1.53 –
(0.017)²} x 5

Ö{1.53 –
0.000289) x 5

= Ö(1.529) x 5

= 1.24 x 5

= 6.2

Standard Deviation = 6.2 (Apprx.)

Comment

The value of range is 22.5,Quartile
Deviation is 4.41, Mean Deviation is 4.94 and Standard Deviation is 6.2.As
Standard Deviation is the most consistent measure of variability, considering
it, it can be said that lower scores are not much dispersed, they remain nearer
to the mean;. From the analysis of Measures of Central Tendency
&Variability some findings can be noted:

29
scores (50%) stand below the mean and 29 scores (50%%) stand above the
mean. So the distribution is supposed to be normal.
The
mean, median and mode are very near to the same. But Mean>Median>Mode.
Most
scores are near the mean and the further from the mean a score is, the
fewer the number of subjects who attained that score.
Mean
± 1.0 S.D., that is, 11.7 – 24.1 contains a total of 39 scores (67.24%).
So the distribution is supposed to be normal

These findings show that
although the distributions of Mean ± 1.0 S.D but the distribution of Mean ± 2.0
S.D. and Mean ± 3.0 S.D is too far from the normal curve. The distribution is
said to be normal and kurtosis.

The distribution is very near to
normal but very little positively skewed

Fig:
Positive Skewness

Skewness of the distribution = 3 (
mean – median ) / S.D = 0.1 (Apprx).

The value is very low which indicates
the distribution is very near to the normal distribution.

The distribution is very near to normal but is very little
platykurtic

Leptokurtic – where more
scores than normal distribution stand in mean ±2.0 & 3.0S.D.

5.1.3
Measures of Relative Positions

Major measures of relative
positions are percentile ranks, Z-score and T-score. I shall determine only
Z-score and T-score here as they are more reliable than percentile ranks.

# Standard score (Z – Score), Z
= (X – M) / s

# T = 50 + 10Z

Student’s Roll No.	Z –score (Z = (X-M)/ s)	T-score (T = 50 + 10Z)
01	(30 – 17.9) / 6.2 = 1.95	69.5
05	(22 – 17.9) / 6.2 = 0.66	56.6
08	(16.5 – 17.9) / 6.2 = – 0.23	47.7
09	(19 – 17.9) / 6.2 = 0.18	51.8
10	(11 – 17.9) / 6.2 = – 1.11	49.9
11	(16 – 17.9) / 6.2 = – 0.30	47
12	(14 – 17.9) / 6.2 = – 0.63	43.7
13	(16 – 17.9) / 6.2 = – 0.30	47
14	(14 – 17.9) / 6.2 = – 0.63	43.7
15	(21 – 17.9) / 6.2 = – 0.50	45
16	(9 – 17.9) / 6.2 = – 1.44	35.6
17	(19 – 17.9) / 6.2 = 0.18	51.8
18	(31.5 – 17.9) / 6.2 = 2.19	71.9
19	(24 – 17.9) / 6.2 = 0.98	59.8
20	(11 – 17.9) / 6.2 = – 1.11	48.9
21	(26.5 – 17.9) / 6.2 = 1.39	63.9
22	(12.5 – 17.9) / 6.2 = – 0.87	41.3
23	(22 – 17.9) / 6.2 = 0.66	56.6
25	(9 – 17.9) / 6.2 = – 1.44	35.6
26	43.4
27	(15 – 17.9) / 6.2 = – 0.47	45.3
28	(26 – 17.9) / 6.2 = 1.30	63
29	(12.5 – 17.9) / 6.2 = –0.87	41.3
32	(17.5 – 17.9) / 6.2 = – 0.06	49.4
33	(8 – 17.9) / 6.2 = – 1.60	34
34	(11.5 – 17.9) / 6.2 = – 1.03	39.7
36	(10 – 17.9) / 6.2 = -1.27	37.3
37	(19.5 – 17.9) / 6.2 = 0.26	52.6
38	(30 – 17.9) / 6.2 = 1.95	69.5
39	(18 – 17.9) / 6.2 = 0.02	50.2
40	(13 – 17.9) / 6.2 = – -0.80	42
41	(20 – 17.9) / 6.2 = 0.34	53.4
42	(24.5 – 17.9) / 6.2 = 1.66	66.6
43	(19 – 17.9) / 6.2 = 0.18	51.8
44	(12 – 17.9) / 6.2 = – 0.95	40.5
45	(12 – 17.9) / 6.2 = – 0.95	40.5

Comment

From this table relative
position of any student in comparison to other or whole as a group can easily
be made. The T-score shown above it is a comprehensive presentation of relative
position. Scores above 50 are more than average; scores below 50 are less than
average.

5.1.4
Grading of Test-1 Results

Norm
of Grading

Norm	Number Range (Apprx)	Grade	GPA
Mean + 2.5 S.D. & above	33 and above	A	4.00
Mean +1.5 S.D. – up to Mean + 2.5 S.D.	27 -32	B	3.50
Mean + 0.5 S.D. – up to Mean + 1.5 S.D.	21 – 26	C	3.00
Mean – 0.5 S.D.-up to Mean + 1.5 S.D.	14 – 19	D	2.50
Below Mean – 0.5 S.D.	0 – 13	F	——

Grading
of students

Roll No.	Obtained Mark	Grade	GPA
01	30	B	3.50
02	22	C	3.00
03	16.5	D	2.50
04	19	D	2.50
05	11	F	——
06	16	D	2.50
07	14	D	2.50
08	16	D	2.50
09	14	D	2.50
10	21	C	3.00
11	9	F	——
12	19	D	2.50
13	31.5	B	3.50
14	24	C	3.00
15	11	F	——
16	26.5	B	3.50
17	12.5	F	——
18	22	C	3.00
19	9	F	——
20	22	C	3.00
21	15	D	2.50
22	26	C	3.00
23	12.5	F	——
24	17.5	D	2.50
25	18	D	2.50
26	11.5	F	——
27	10	F	——
28	19.5	D	2.50
29	30	B	3.50
30	18	D	2.50
31	13	F	——
32	20	D	2.50
33	24.5	C	3.00
34	19	D	2.50
35	12	F	——
36	12	F	——
37	18	D	2.50
38	18	D	2.50
39	15	D	2.50
40	23	C	3.00
41	19	D	2.50
42	23.5	C	3.00
43	11.5	F	——
44	22	C	3.00
45	28.5	B	3.50

It
is to be noted that this grading was not executed in the school’s test result;
it is done only to fulfill the purpose of statistical analysis report. Combined
score of MCQ and Essay type test was executed for grading of students and that
result was submitted to school. Then the score was converted into 15 and was
added as class test number

Percentage of pass and
Fail

P/F	No. of students	Percentage
Pass	40	69%
Fail	18	31%

Percentage of grading

Grade	No. of students	Percentage
A	0	0%
B	6	10.34%
C	14	24.14%
D	20	34.48%
F	18	31.04%

5.1.5 Graphic presentation of Test-1
result analysis

5.2 Analysis of Test-2 results (MCQ
test)

Student’s score in Test-2

Roll No.	Name	Obtained Mark (out of 50)
01	Parvin Akter Sumi	26
05	Tania Akter	29
08	Rawnok Sultana	29
09	Farhana Akter	22
10	Afroza Akter Anika	22
11	Farzana Abedin Chadni	18
12	Shahana Akter Runa	22
13	Mahmuda Akter Asha	23
14	Ivy Moni	21
15	Aesha Akter Lucky	22
16	Moni Akter	20
17	Sabina Yasmin Boishakhi	23
18	Shompa Akter	27
19	Shakil Hossain	25
20	Soleman Hossain	20
21	Aesha Akter Liza	27
22	Surma Akter	20
23	Md. Rubel	23
25	Kohinur Akter Munni	19
26	Eti Rani Das Brishti	24
27	Shamsun Nahar	24
28	Kamrul Hasan Meraj	26
29	Nur Fatema	19
32	Tania Akter	16
33	Bithi Akter Nadia	22
34	Jasim Uddin	21
36	Shima Akter Shimu	21
37	Rita Rani Roy	23
38	Maksuda Akter Priya	28
39	Mominur Parvez Rafil	20
40	Shahadat Hossain	22
41	Sazzad Hossain	18
42	Alamin Mia	23
43	Miraj Hossain Shuvo	22
44	Shongita Rani Roy	27
45	Nargis Akter	20

Tabulation of scores

# Number of the class = (Range/class Interval) +1

= 3.2 + 1

Frequency Distribution Table

Class Interval (C.I.)	Tallies	Frequency
11 -15	\|	1
16 – 20	\|\|\|\| \|\|\|\| \|\|\|\|	14
21 – 25	\|\|\|\| \|\|\|\| \|\|\|\| \|\|\|\| \|\|\|\| \|\|\|\|	30
26 – 30	\|\|\|\| \|\|\|\| \|\|\|	13

5.2.1 Measures of Central Tendency

5.2.1.1 The Mean

# True Mean = A.M.+(Σfd/N)i

C.I.	Mid point	Frequency (f)	Deviation (d)	Product (fd)
11 -15	13	1	-2	– 2
16 – 20	18	14	– 1	– 14
21 – 25	23	30	0	0
26 – 30	28	13	+ 1	+ 13

N = 58 Σfd = -3

Here –

A.M.= 23

N = 58

Σfd = – 3

i = 5

True Mean =
A.M.+(Σfd/N)i

23 + (- 3/58) 5

5.2.1.2 The Median

# Median = L+{(N/2-cfu)/fm}I

C.I.	Lower and upper limit of C.I.	Frequency (f)	Cumulative Frequency (cfu)
11 -15	10.5 – 15.5	1	1
16 – 20	15.5 – 20.5	14	15
21 – 25	20.5 – 25.5	30	45
26 – 30	25.5 –30.5	13	58

Here-

L = 20.5

Cfu = 15

fm = 30

i = 5

N = 58

Median =
L+{(N/2-cfu)/fm}i

= 20.5 +{(29 – 15)/ 29} 5

= 20.5 + (14/29) 5

Median = 22.9

5.2.1.3
The Mode

Mode = 3 median – 2 mean

Mode = 23.2

Comment

The value of mean, median and
mode is respectively 22.75, 22.9 and 23.2.The values of mean and median and
mode are nearer to each other. Here 21 – 25 class interval contains maximum
number of frequency, mode, mean and median belong to that class interval.16 –
20 , 21 – 25 and 26 – 30 class intervals contain a total of 57 scores together,
that is 98.28% of the total score. It shows that the scores have very high
central tendency.

5.2.2 Measures of Variability

5.2.2.1 The Range

Range = 16

5.2.2.2 The Quartile Deviation

# Q₁ = L₁ + {(N/4-F₁)/fq₁}I

Here-

L₁
= 15.5

F₁
= 1

fq₁
= 14

i
= 5

N = 58

Q₁ = L₁ + {(N/4-F₁)/fq₁}
i

= 15.5
+{(14.25 – 1)/14} 5

= 15.5 + {(13.25)/14} 5

= 15.5 +
(0.95) 5

= 15.5 + 4.75

= 20.25

# Q₃ = L₃ + {(3N/4 – F₃)/fq₃}
i

Here-

L₃ = 20.5

fq₃ = 30

N = 58

Q₃ = L₃ +
{(3N/4 – F₃)/fq₃} I

=
20.5 + (0.96) 5

=
20.5 + 4.8

= 30.3

Quartile Deviation, Q = ( Q₃–
Q₁)/2

= (30.3 – 20.25)/2

= 10.05/2

= 5.03

Quartile
Deviation = 5.03 (Apprx.)

5.2.2.3
Mean Deviation

S||
/N

C.I.	Mid point (X)	Mean	f	d = x – M	fd
11 -15	13	22.75	1	– 9.75	– 9.75
16 – 20	18	22.75	14	– 4.75	+ 66.5
21 – 25	23	22.75	30	+ 0.75
26 – 30	28	22.75	13	+ 5.25	+ 68.25

S||
= 145.25

Here-

S|fd| = 145.25

N = 58

S||
/N

=
145.25/58

= 2.50

Mean Deviation = 2.50 (Apprx.)

5.2.2.4 Standard Deviation

s
= ÖSfd²/N
– (Sfd/N)²}I

C.I.	f	Deviation (d)	fd	fd²
11 -15	1	-2	– 2	+ 4
16 – 20	14	– 1	– 14	+14
21 – 25	30	0	0	0
26 – 30	13	+ 1	+ 13	13

∑fd = – 3

∑fd²=31

i =5

N = 58

sÖSSfd/N)²}i

Ö{31/58 –
(- 3/58)²} x 5

Ö{0.53 –
(0.05)²} x 5

Ö{0.53 – 0.0025}
x 5

= Ö(0.53) x 5

= 0.73 x 5

= 3.65

Standard Deviation = 3.65 (Apprx.)

Comment

The value of range is 16,Quartile
Deviation is 5.03, Mean Deviation is 2.50 and Standard Deviation is 3.65.As
Standard Deviation is the most consistent measure of variability, considering
it, it can be said that lower scores are not much dispersed, they remain nearer
to the mean.. From the analysis of Measures of Central Tendency
&Variability some findings can be noted:

30
scores (51.72%) stand below the mean and 28 scores (47.28%) stand above
the mean. So the distribution is nearly normal.

The
mean, median and mode are not the same. Mean>Median>Mode.

Most
scores are near the mean and the further from the mean a score is, the
fewer the number of subjects who attained that score.

Mean
± 1.0 S.D., that is, 19.1 – 26.4 contains a total of 38 scores (65.51%).
So the distribution is nearly normal.

These findings show that
although the distributions not so far from the normal distribution and it are a
little negatively skewed also.

The distribution is very near to
normal & very little negatively
skewed

Fig: Negative
Skewness

Skewness of the distribution = 3 (mean – median) /
S.D = – 0.04

The value of skewness is very low and therefore
ignorable.

The distribution is very nearly normal

Fig: Normal
Distribution

5.2.3
Measures of Relative Positions

Major measures of relative
positions are percentile ranks, Z-score and T-score. I shall determine only
Z-score and T-score here as they are more reliable than percentile ranks.

# Standard score (Z – Score), Z
= (X – M) / s

# T = 50 + 10Z

Student’s Roll No.	Z –score (Z = (X-M)/ s)	T-score (T = 50 + 10Z)
01	(26 – 22.75) / 3.65 = 0.89	58.9
05	(29 – 22.75) / 3.65 = 1.67	66.7
08	(29 – 22.75) / 3.65 = 1.67	66.7
09	(22 – 22.75) / 3.65 = – 0.20	48
10	(22 – 22.75) / 3.65 = – 0.20	48
11	(18 – 22.75) / 3.65 = – 1.30	37
12	(22 – 22.75) / 3.65 = – 0.20	48
13	(23 – 22.75) / 3.65 = 0.07	50.7
14	(21 – 22.75) / 3.65 = – 0.48	45.2
15	(22 – 22.75) / 3.65 = – 0.20	48
16	(20 – 22.75) / 3.65 = – 0.75	42.5
17	(23 – 22.75) / 3.65 = 0.07	50.7
18	(27 – 22.75) / 3.65 = 1.16	61.6
19	(25 – 22.75) / 3.65 = 0.62	56.2
20	(20 – 22.75) / 3.65 = – 0.75	42.5
21	(27 – 22.75) / 3.65 = 1.16	61.6
22	(20 – 22.75) / 3.65 = – 0.75	42.5
23	(23 – 22.75) / 3.65 = 0.07	50.7
25	(19 – 22.75) / 3.65 = – 1.03	38.7
26	(24 – 22.75) / 3.65 = 0.34	53.4
27	(24 – 22.75) / 3.65 = 0.34	53.4
28	(26 – 22.75) / 3.65 = 0.89	58.9
29	(19 – 22.75) / 3.65 = – 1.03	39.7
32	(16 – 22.75) / 3.65 = – 1.85	31.5
33	(22 – 22.75) / 3.65 = – 0.20	48
34	(21 – 22.75) / 3.65 = – 0.48	45.2
36	(21 – 22.75) / 3.65 = -0.48	45.2
37	(23 – 22.75) / 3.65 = 0.07	50.7
38	(28 – 22.75) / 3.65 = 1.44	64.4
39	(20 – 22.75) / 3.65 = – 0.75	42.5
40	(22 – 22.75) / 3.65 = – 0.20	48
41	(18 – 22.75) / 3.65 = -1.30	37
42	(23 – 22.75) / 3.65 = 0.07	50.7
43	(22 – 22.75) / 3.65 = – 0.20	48
44	(27 – 22.75) / 3.65 = 1.16	61.6
45	(20 – 22.75) / 3.65 = – 0.75	42.5

Comment

From this table relative
position of any student in comparison to other or whole as a group can easily
be made. The T-score shown above itself is a comprehensive presentation of
relative position. Scores above 50 are more than average, scores below 50 are
less than average.

5.2.4
Grading of Test-1 Results

Norm
of Grading

Norm	Number Range (Apprx)	Grade	GPA
Mean + 3 S.D. & above	34 and above	A	4.00
Mean + 1.5 S.D. – up to Mean + 3 S.D.	28 – 33	B	3.50
Mean + 0.5 S.D. – up to Mean +1.5 S.D.	23 – 27	C	3.00
Mean – up to Mean – 1.5 S.D.	17 – 22	D	2.50
Below Mean – 1 S.D.	0 – 16	F	——

Grading
of students

Roll No.	Obtained Mark	Grade	GPA
01	26	C	3.00
05	29	B	3.50
08	29	B	3.50
09	22	D	2.50
10	22	D	2.50
11	18	D	2.50
12	22	D	2.50
13	23	C	3.00
14	21	D	2.50
15	22	D	2.50
16	20	D	2.50
17	23	C	3.00
18	27	C	3.00
19	25	C	3.00
20	20	D	2.50
21	27	D	2.50
22	20	D	2.50
23	23	C	3.00
25	19	D	2.50
26	24	C	3.00
27	24	C	3.00
28	26	C	3.00
29	19	D	2.50
32	16	F	——
33	22	D	2.50
34	21	D	2.50
36	21	D	2.50
37	23	C	3.00
38	28	B	3.50
39	20	D	2.50
40	22	D	2.50
41	18	D	2.50
42	23	C	3.00
43	22	D	2.50
44	27	C	3.00
45	20	D	2.50

It is to be noted that this grading was not executed in the
school’s test result; it is done only to fulfill the purpose of statistical
analysis report. Combined score of MCQ and Essay type test was executed for
grading of students and that result was submitted to school. Then the score was
converted into 15 and was added as class test number.

Percentage of pass and
Fail

P/F
No. of students
Percentage
Pass
55
94.83%
Fail
3
5.17%

Percentage of grading

Grade
No. of students
Percentage
A
0
0%
B
4
6.9%
C
23
39.65%
D
28
48.27
F
3
5.17%

N
SSSY¡ÖSX² – (SX )² }{ NSY² – ( SY )² }

Roll No	Score of Test-1 ( X )	X²	Score of Test-2 ( Y )	Y²	XY
01	30	900	26	676	780
05	22	484	29	841	638
08	16.5	272.25	29	841	478.5
09	19	361	22	484	418
10	11	121	22	484	242
11	16	256	18	324	288
12	14	196	22	484	308
13	16	256	23	529	368
14	14	196	21	441	294
15	21	441	22	484	462
16	9	81	20	400	180
17	19	361	23	529	437
18	31.5	992.25	27	729	850.5
19	24	576	25	625	600
20	11	121	20	400	220
21	26.5	702.25	27	729	715.5
22	12.5	156.25	20	400	250
23	22	484	23	529	506
25	9	81	19	361	171
26	22	484	24	576	528
27	15	225	24	576	360
28	26	676	26	676	676
29	12.5	156.25	19	361	237.5
32	17.5	306.25	16	256	280
33	18	324	22	484	396
34	11.5	132.25	21	441	241.5
36	10	100	21	441	210
37	19.5	380.25	23	529	448.5
38	30	900	28	784	840
39	18	324	20	400	360
40	13	169	22	484	286
41	20	400	18	324	360
42	24.5	600.25	23	529	563.5
43	19	361	22	484	418
44	12	144	27	729	324
45	12	144	20	400	240
N = 45	S X = 1038	SX² = 20677	S Y = 1313	SY² = 30441	S XY = 24178.5

N
SSSY¡ÖSX² – ( SX )² }{ NSY² – ( SY )² }

Ö [{ 58 x 20677 – ( 1038 )² }{ 58 x 30441 –
( 1313 )² }]

=Ö ( 1199266 – 1077444 )(
1765578 – 1723969 )Ö 121822 x 41609== + 0.55 (Apprx.)

Correlation = + 0.55

Comment

The value of correlation between
Test-1 & Test-2 is +0.55. That indicates the tests have a positive,
substantial and marked relationship. The two tests scores have a tendency to
vary in the same direction. For example: a student who has done well in test-1
has a high chance to do well in Test-2 and a student who could not do well in
Test-1 has a high chance to score low in Test-2 and vise versa. This
relationship is substantial and marked.

5.4 Graphic comparison between Test-1
& Test-2 results

PATEL
R.N., Educational Evaluation, New Delhi: Himalaya Publishing House, 1985.

BLOMMWRS
Paul and LINDQUIST. E.F., Elementary Statistical Methods, University of
London Press Ltd.

THORNDIKE
R.L. and ELIZABETH H.H., Measurement and Evaluation in Psychology and
Education, Wiley Eastern Pvt. Ltd. New Delhi.

GARRET
H.F. Statistics in Psychology and Education.

TAPAN
SHAJAHAN and HOSSAIN MONIRA, Educational Evaluation, School of Education,
Bangladesh Open University, 1998.

Syllabus

Subject

Comment

Subject

Comment

Manipulation of Data According to formula

Manipulation of Data According to formula

Reliability =0.08 (Apprx) ; Test’s Reliability is low

5.1.1.3 The Mode

5.1.2.3 Mean Deviation

Comment

The distribution is very near to normal but is very little platykurtic

5.1.3 Measures of Relative Positions

P/F

Mode = 23.2

P/F

XY

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Reliability =0.08 (Apprx) ;
Test’s Reliability is low

5.1.1.3
The Mode

5.1.2.3
Mean Deviation

The distribution is very near to normal but is very little
platykurtic

5.1.3
Measures of Relative Positions