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Transcript of Adaptation of the Otis-Lennon Mental Ability Test...
CHAPTER IV
Adaptation of the Otis-Lennon Mental Ability Test
(OLMAT)
As stated earlier, one of the objectives of this study is to ascertain whether or
not there would be a significant relationship between mental ability (intelligence)
scores of the Yemeni students and their age, sex, and school achievement. However,
before studying this aspect in detail, the present chapter aims at adapting Otis-Lennon
Mental Ability Test (OLMAT) on the Yemeni sample.
Therefore, in this chapter, the results of the adaptation of mental ability test
are presented in the following order:
1. Psychometric properties of the items, like difficulty and discrimination
indices.
2. The test reliability and validity indices.
3. The norms for the adapted version of the Yemeni culture.
The Arabic version of OLMAT advanced level form (K) was administered to
a random sample of 1561 students that included 801 males, and 760 females, from
government schools in Sana’a city from Yemen.
75
4.I. PSYCHOMETRIC PROPERTIES OF THE ITEMS,
DIFFICULTY AND DISCRIMINATION, FOR THE TEST
ITEMS.
4.1.1. Item difficulty:
The item difficulty is defined in terms of the percentage of students who
answer it correctly. In this study the item difficulty was calculated according to
grades X, XI and XII for each subtest and for the total test. Table 4-1 presents the
frequency distribution for the items difficulty in each subtest and total test according
to grade levels. Appendix (5) shows the items difficulty for all the items according to
grade for each subtest and total test.
76
Table 4-1:
Frequency Distribution of the items’ difficulty according to grade levels and total sample for each subtest.
Class
Interval
Verbal comprehension Verbal reasoning Figural reasoning Quantitative reasoning Total test
X XI XII tota
l
X XI XII Tot
al
X XI XII Tot
al
X XI XII tota
l
X XI XII Total
0.20 – 0.29 2 - - - 7 1 - - 5 1 - 1 2 2 - 2 16 4 - 3
0.30 – 0.39 6 5 - 4 9 7 2 6 3 4 3 4 8 2 2 1 26 18 7 15
0.40 – 0.49 5 5 4 6 5 5 4 9 5 3 1 2 2 3 - 6 17 16 9 23
0.50 – 0.59 5 4 5 5 2 7 6 6 2 5 1 6 2 6 5 3 11 22 17 20
0.60 – 0.69 3 5 4 3 2 4 5 4 - 1 8 1 - - 3 2 5 10 20 10
0.70 – 0.79 4 4 4 5 - 1 8 - - 1 - 1 1 1 2 1 5 7 14 7
0.80 – 0.89 - 2 7 2 - - - - - - 1 - - 1 3 1 1 3 11 2
0.90 – 0.99 - - 1 - - - - - - - 1 - - - - - - - 2 -
N. Items 25 25 25 25 25 25 25 25 15 15 15 15 15 15 15 15 80 80 80 80
Mean
difficulties
0.49 0.56 0.67 0.56 0.37 0.48 0.59 0.46 0.38 0.47 0.60 0.46 0.38 0.49 0.63 0.48 0.41 0.51 0.62 0.50
77
The items’ difficulty in grade X ranged from 0.21 to 0.75 with a mean of 0.41,
in grade XI it ranged from 0.21 to 0.83 with a mean of 0.51, and in grade XII it ranged
from 0.32 to 0.92 with a mean of 0.62 and in the total sample it ranged from 0.25 to
0.81 with a mean of 0.50.
4.1.2. Item Discrimination
Item discrimination refers to the degree to which an item differentiates
correctly among test takers in the behavior that the test is designed to measure. In the
present study, the point biserial correlation (r pbs) between each item response and the
total test score were calculated according to grades (X, XI, XII) for each subtest and
for the total test. Table 4-2 presents the frequency distribution for the items’
discrimination in each subtest and total test according to grade levels. Appendix (6)
shows the items’ discrimination for all items, according to grades, for each subtest and
the total test.
78
Table 4-2:
Frequency Distribution of the items’ discrimination according to grade level and total sample in each subtest
Class Interval
Verbal comprehension Verbal reasoning Figural reasoning Quantitative reasoning Total test
X XI XII Tot
al
X XI XII Tot
al
X XI XII Tot
al
X XI XII tota
l
X XI XII total
0.20 – 0.29 4 - - 2 2 - - 1 - - - 1 1 - - 1 7 - - 5
0.30 – 0.39 14 3 4 10 12 1 2 11 7 1 - 6 7 1 1 7 40 6 7 34
0.40 – 0.49 4 9 9 10 7 14 11 8 2 6 7 1 4 7 7 2 17 36 34 21
0.50 – 0.59 2 10 6 - 3 7 7 3 3 2 2 1 2 3 4 2 10 22 19 6
0.60 – 0.69 - 2 4 3 1 2 3 2 3 3 2 5 - 3 - 1 4 10 9 12
0.70 – 0.79 1 1 1 - - 1 2 - - 3 3 1 1 - 2 1 2 5 8 2
0.80 – 0.89 - - 1 - - - - - - - 1 - - 1 1 - - 1 3 -
N. Items 25 25 25 25 25 25 25 25 15 15 15 15 15 15 15 15 80 80 80 80
Mean
discrimination
0.38 0.49 0.52 0.41 0.40 0.49 0.51 0.42 0.45 0.55 0.58 0.48 0.42 0.53 0.53 0.46 0.41 0.51 0.53 0.44
79
The item discriminations in grade X ranged from 0.24 to 0.75 with a mean of
0.41, in grade XI the range was from 0.35 to 0.83 with a mean of 0.51, in XII it
ranged from 0.34 to 0.88 with a mean of 0.53, and in the total test it ranged from 0.24
to 0.78 with a mean of 0.44.
4.2. THE TEST RELIABILITY AND VALIDITY INDICES.
4.2.1. The Test Reliability
Reliability is considered to be one of the very important psychometric
characteristics of the test. Reliability refers to the consistency of scores obtained by
the same persons, when they are reexamined with the same test on different
occasions, or with different sets of equivalent items, or under other variable
examining conditions (Anastasi & Urbina, 2003).
The reliability of the test was obtained by two methods, Split – Half Method,
Test – Retest Method.
4.2.1.1. Split – Half Method
This type of reliability coefficient is sometimes called a coefficient of internal
consistency, for this only a single administration of a single form is required. To find
split-half reliability, the first problem is how to split the test in order to obtain the
most nearly equivalent halves. The test starts with the easiest items and then becomes
progressively more difficult. In splitting a test, the two halves would need to be as
80
similar as possible. Therefore, the simplest method of approximating this goal is to
adopt an odd – even split, in which the odd – numbered items or one half of the test
and the even – numbered items form the other. This guarantees that each half will
contain an equal number of items from the beginning, middle, and end of the original
test. In this case the odd-even procedure was followed. The correlation between two
halves was calculated for each level and for the total test. The value was 0.86 for total
test and for different levels (X, XI, and XII), the values were 0.77, 0.75, and 0.83
respectively. These correlations would be a reasonable measure of the reliability of
one half of the test. The reliability of the entire test would be greater than the
reliability of either half taken alone. The Spearman – Brown formula can be used to
obtain the reliability of the whole test (Allen & Yen, 1979). The corrected reliability
coefficients obtained by Spearman – Brown formula, for the different levels (X, XI,
XII) and total test were as follows, 0.87, 0.86, 0.91, and 0.92 consecutively.
4.2.1.3. Test – Retest Method
The reliability coefficients found by this method is an index to the stability of
test results. After two weeks from the test administration the intelligence test was
administered again to 241 students, which included (106) X, (76) XI, and (59) XII std
students, and the Pearson’s correlation coefficients were calculated between the
scores of the students in first and second administrations. The obtained values of the
reliability were as follows: 0.83 for total test, and 0.74, 0.88, and 0.82 for X, XI, XII,
levels respectively.
81
4.2.2. The Test Validity
The most crucial characteristic of intelligence tests is their validity. Validity
refers to how well a test measures what it is supposed to measure. There are different
types of validities for intelligence tests. In the present research three types of
validities were obtained viz. construct validity, concurrent validity, and discriminant
validity.
4.2.2.1. Construct validity:
The construct validity was obtained by computing the correlation coefficient
between the items with the total test, and between the subtests (dimensions). Besides,
the correlations of the subtests with each other and with the total test, the correlation
values between the items with subtests were positive at all levels, and the correlation
between the item with its subtests was higher than its correlation with the total test.
This is because the items included in the same subtest (dimension) have more
internal-consistency with each other.
Also the results revealed that the correlation coefficients between the items
and the total test were positive which indicate the construct validity. In addition
correlation coefficients between subtests and total test were higher than the
correlation coefficient values between subtests. This is because each subtest measures
one side of the general mental ability. Table 4-3 presents values of subtests
correlation coefficient with each other at different levels of grade and with total test.
All the values were positive and significant.
82
Table 4-3: Correlation coefficients between subtests with each other and with total
test according to levels of grade.
Level of
grade
Subtest Total
test
Verbal
Compre
hension
Verbal
Reasoning
Figural
Reasoning
Tenth grade
(X)
(N = 682)
Verbal comprehension 0.82** --
Verbal reasoning 0.87** 0.60** --
Figural reasoning 0.80** 0.52** 0.61** --
Quantitative reasoning 0.77** 0.49** 0.57** 0.58**
Eleventh
grade1 (XI)
(N = 466)
Verbal comprehension 0.88** -
Verbal reasoning 0.90** 0.71** -
Figural reasoning 0.87** 0.65** 0.72**
Quantitative reasoning 0.83** 0.63** 0.65** 0.71**
Twelfth
grade (XII)
(N = 413)
Verbal comprehension 0.88** -
Verbal reasoning 0.90** 0.70** -
Figural reasoning 0.89** 0.67** 0.74** -
Quantitative reasoning 0.86** 0.65** 0.71** 0.76**
Entire
Sample
(N = 1561)
Verbal comprehension 0.88** -
Verbal reasoning 0.91** 0.73** -
Figural reasoning 0.88** 0.67** 0.74** -
Quantitative reasoning 0.87** 0.67** 0.72** 0.74**
A detailed analysis of Table (4-3) indicates that correlation coefficient values
between subtests and total test is higher than correlation coefficient values between
subtests with each other.
83
4.2.2.2. Concurrent validity.
The concurrent validity was calculated by computing the correlation between
students’ scores on the intelligence test and their school achievement.
Table 4.4 presents the Pearson Correlation Coefficients between intelligence
scores and school achievement for each subtest and for the total test according to
grade levels, X, XI, and XII. All of these correlations are significant at the (0.01)
level. It is clear therefore, that the tests have high concurrent validity.
Table 4-4: Pearson’s correlations coefficients values between intelligence test
scores and school achievement scores.
Grade
Subtests
X grade XI grade XII grade Total
sample
Verbal Comprehension 0.68** 0.75** 0.74** 0.68**
Verbal Reasoning 0.71** 0.75** 0.71** 0.67**
Figural Reasoning 0.61** 0.67** 0.71** 0.62**
Quantitative Reasoning 0.62** 0.61** 0.67** 0.58**
Total Test 0.81** 0.81** 0.80** 0.73**
4.2.2.3. Discriminant validity:
84
The discriminant validity was obtained by using one way analysis of variance,
ANOVA, for different levels of grade. This made sure of the capacity of the test to
distinguish between students in different levels of grade.
Table 4-5: Results of one way ANOVA for students’ scores according to
grade levels.
Source of
Variation
df Sum of Squares Mean Square F P
Between grade 2 71195.295 35597.648 250.492 0.000
Within grade 1558 221408.5 142.111
Total 1560 292603.8
Inspection of table 4-5 indicates that there are significant differences in grade
means at 0.000 level. Table 5-6 presents the results of post hoc tests to find out which
of the means were significantly different from others. The post hoc comparisons
indicated that there are significant differences between means of all grades at 0.000
level.
Table 4-6: Results of Sheffe’s post-hoc comparison between mean of students
scores according to grade.
85
Grade Means Sd X XI XII
X 33.09 10.16 -
XI 40.39 13.24 0.000 -
XII 49.69 13.00 0.000 0.000 -
4.3. THE NORMS FOR THE ADAPTED VERSION ON THE
YEMENI CULTURE
Scores on intelligence tests are most commonly interpreted by reference to
norms that represent the test performance of the standardization sample. The norms
are thus empirically established by determining what persons in a representative
group actually do on the test. Any individual’s raw score is then refereed to the
distribution of scores obtained by the standardization (Anastasi & Urbina, 1999).
There are age norms, grade norms, and group norms. The authors of OLMAT
recommended that the Otis-Lennon tests should provide normative data based upon
the performance of pupils in both age and grade reference groups.
Norms for performance by age: One meaningful frame of reference for
interpretation of scores earned on the Otis-Lennon tests is the pupil’s chronological
age group. When his/her test score is compared with the scores earned by pupils of
similar chronological age tested in the standardization sample, the Deviation IQ
(DIQ) and its associated Percentile-Rank and Stanine equivalent supplied to the
teacher, counselor, or administrator are an indication of his/her level of performance.
86
Norms for performance by grade: A second general frame of reference for the
interpretation of scores earned on the Otis-Lennon tests is the pupil’s grade group.
The grade Percentile-Rank and Stanine scores indicate the level of pupil performance
when his/her test score is compared with the scores earned by pupils who were at the
same grade level in the standardization sample.
There are various types of scores that are used to report norms, for example,
Percentile-Ranks, Stanines, Grade Equivalents, and Standard scores. All of them are
types of score, derived from raw scores, to report normative performance.
4.3.1. Percentile - Rank
The percentile rank is one of the most widely used means of interpreting pupil
performance on standardized measures of ability and achievement. This particular
type of derived score shows, in effect, the relative rank of a given pupil when his/her
score is compared with those earned by pupils comprising a particular reference, or
norms, group. For example, if a pupil earned a DIQ score of 116 with its
corresponding percentile rank of 84, this means that 84 percent of the pupils in the
norming sample earned DIQs of 116 or less, while 16 percent earned DIQs higher
than 116. A DIQ score of 100 corresponds to a percentile rank of 50, representing the
middle, or average, DIQ for pupils of the same age in the normative group.
Percentile-rank norms have an appeal which stems from their ease of
interpretation. There are, however, certain cautions which warrant consideration in
the interpretation of these scores. The units of the percentile-rank score system are not
equal; for example, the difference in ability represented by the difference between
87
percentile ranks of 90 and 95 is much greater, than that represented by the difference
between percentile ranks of 50 and 55. This characteristic of the percentile-rank scale
results from the fact that most scores are concentrated near the middle of a given
score distribution, while relatively few fall at the extremes. Thus, percentile ranks are
useful for describing a pupil’s relative position within a particular reference group,
but they are not useful in expressing differences between the score of one pupil and
that of another pupil.
4.3.2. Standard scores ( z- score)
Standard scores have a mean of 0 and a standard deviation of 1. (A standard
score indicates how many standard deviations from the mean a score lies). For
example, if z = +1, the raw score lies one standard deviation above the mean; if z =
-2, the raw score is two standard deviations below the mean. One major disadvantage
of standard scores is that about half of the scores are negative. Most people prefer not
to deal with negative numbers, because transcription and mathematical errors are
more common (negative signs are easily lost) and because examinees dislike having
negative scores. For these reasons, standard scores generally are not used in reporting
scores.
4.3.3. Deviation IQs
The Otis-Lennon Deviation IQ (DIQ) is, in effect, a normalized standard score
with a mean of 100 and a standard deviation of 16 points. The DIQ is an index of the
88
pupil’s relative brightness when he is compared with pupils of similar chronological
age, regardless of grade placement. The Otis-Lennon DIQ reflects, at a given point in
time, the pupil’s ability to deal with abstract relationships involving the manipulation
of ideas expressed in verbal, numerical, figural, or symbolic form.
4.3.4. Standardized score (T- score)
Any set of standard scores can be transformed to have an arbitrary mean, µ,
and standard deviation, o, by applying the formula Y = oz + µ, where z is the standard
score and Y is the standardized score. T-score is a standardized score with a mean of
50 and a standard deviation of 10.
4.3.5. Stanine
Stanine is a normalized standard score having a mean of 5 and a standard
deviation of 2 points. These scores are expressed as single digits ranging from a low
of 1 to a high of 9, with the nine units of the stanine scale representing essentially
equal distances along the base line of the curve of normal distribution. This, in effect,
means that a stanine of 7 is much better than a stanine of 6 and a stanine 4 is better
than 3.
4.3.6. Mental-age equivalents
This represents the typical, or median, level of performance of pupils of a
given chronological age in the normative sample. For example, a mental-age
89
equivalent of 8- 0 for a certain raw score means that this raw score was the typical, or
median, score earned by 8- year-old pupils tested in the standardization sample.
The raw – scores transformations transform scores in order to make them
more meaningful. In most cases, this meaning is derived by comparing a student’s
performance with other students. Transformations of scores are of two basic types:
linear and nonlinear. A linear transformation can be defined by a linear equation of
the form Y= a X+ b where a and b are constants, X is the raw score, and Y is the
transformed score. In making this transformation, every examinee’s X is transformed
to a Y using linear rule. For example, if Y= 3X – 2, the transformed score
corresponding to a raw score of 12 is 3(12) – 2=34. When raw scores are linearly
transformed, the shape of the distribution of the transformed scores is the same as the
shape of the distribution of the raw scores (Allen & Yen, 1979).
A nonlinear transformation will change the shape of the raw scores’
distribution. The transformation by this way involves forcing the distribution of
transformed scores to be as close as possible to a normal distribution by smoothing
out, stretching or condensing irregularities and departures from normality in the raw
score distribution. This transformation can be reasonably applied if the test developer
believes that the underlying trait has a normal distribution and that the no normality
of the raw score distribution represents error due to sampling or test – construction
problems (Allen and Yen, 1979). A nonlinear transformation was used in this current
research. The normalization process involves several steps:
1. Transform the score to percentiles.
90
2. Find the grade score in the normal distribution corresponding to each
percentile.
3. (Optional) transform these standard scores to standardized scores with a
desired mean and standard deviation.
Tables 4-7 and 4-8 present the relationship between Percentile, Stanine, and
Deviation Intelligence Quotient (DIQ) for grade levels and age levels, and Tables 4-9
to 4-17, present the Raw-scores, Percentile Ranks, z-scores, T-scores, Deviation
Intelligence Quotient (DIQ), and Stanine for grades and, ages and total sample, which
were transformation by nonlinear transformation.
Table 4- 7: Present the relationship between Percentile Rank, Stanine, DIQ for grade
levels, after nonlinear transformation.
Percentile
Rand
Stanine DIQ X DIQ XI DIQ XII Interpretation
0 – 4% 1 52 – 70 52 – 69 54 -72 Low
5% - 11% 2 70 – 77 69 – 80 72 – 79 Below
Average12% - 23% 3 77 – 85 80 – 88 79 – 88
24% - 40% 4 85 – 96 88 – 95 88 – 95
Average41% - 60% 5 96 – 103 95 – 103 95 – 104
61% - 77% 6 103 – 111 103 – 112 104 – 111
78% - 89% 7 111 – 119 112 – 120 111 – 120 Above
Average90% - 96% 8 119 – 128 120 – 127 120 – 126
97% - 100% 9 128 – 148 127 – 148 126 – 148 High
Table 4-8: Presented the relationship between Percentile Rank, Stanine, DIQ for age
levels after nonlinear transformation.
Percentile
Rank
Stanine DIQ 15
age
DIQ 16
age
DIQ 17
age
DIQ 18
age
DIQ
19 age
Interpreta-
ion
91
0 – 4% 1 60-71 56-71 56-71 60-68 67-70 Low
5% - 11% 2 71-79 71-78 71-79 68-78 70-79 Below
Average12% - 23 3 79-87 78-87 79-86 78-88 79-88
24% - 40% 4 87-96 87-95 86-95 88-96 88-96
Average 41% - 60% 5 96-104 95-103 95-103 96-104 96-103
61% - 77% 6 104-112 103-112 103-111 104-112 103-111
78% - 89% 7 112-118 112-120 112-119 112-120 111-119 Above
average90% - 96% 8 118-127 120-128 119-126 120-127 119-127
97%-100% 9 127-148 128-148 127-148 127-148 127-148 High
Table 4–9: Row scores and their equivalent, Percentile Rank, z- scores, T- scores,
Deviation Intelligence Quotient (DIQ), and Stanine for Total sample.
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
12 0.1 -3.0 20 52 -0.1
15 0.4 -2.65 23.5 57.6 -0.3
16 1.0 2.40 26 61.6 0.2
17 1.4 -2.20 28 64.8 0.6
18 2.4 -1.98 30.2 68.32 1.04
19 3.8 -1.77 32.3 71.68 1.46
20 5.9 -1.65 33.5 73.6 1.7
21 8.2 -1.39 36.1 77.76 2.22
Table 4–9: Continued
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
22 10.0 -1.29 37.1 79.36 2.42
23 11.0 -1.23 37.7 80.32 2.54
92
24 12.2 -1.17 38.3 81.28 2.66
25 15.1 -1.03 39.7 83.52 2.94
26 18.2 -0.91 40.9 85.44 3.18
27 21.1 -0.81 41.9 87.04 3.38
28 22.8 -0.74 42.6 88.16 3.52
29 24.2 -0.70 43 88.8 3.60
30 25.0 -0.65 43.5 89.6 3.76
31 30.0 -0.53 44.7 91.52 3.94
32 33.8 -0.42 45.8 93.28 4.16
33 39.0 -0.28 47.2 95.52 4.44
34 40.2 -0.25 57.5 96 4.50
35 44.3 -0.14 48.6 97.76 4.72
36 49.1 -0.03 49.97 99.52 4.94
37 51.4 0.04 50.4 100.64 5.08
38 53.8 0.10 51 101.6 5.20
39 56.8 0.17 51.7 102.72 5.34
40 59.6 0.24 52.4 103.84 5.48
41 61.6 0.29 52.9 104.64 5.58
42 63.2 0.34 53.4 105.44 5.68
43 65.8 0.41 54.1 106.56 5.82
44 67.8 0.47 54.7 107.25 5.94
45 70.2 0.53 55.3 108.48 6.06
46 71.2 0.56 55.6 108.96 6.12
47 72.8 0.61 56.1 109.76 6.22
48 74.2 0.65 56.5 110.40 6.30
Table 4–9: Continued
Raw-
scores
Percentile
ranks
z- scores T- scores DIQ Stanine
49 75.4 0.69 56.9 111.04 6.38
93
50 76.9 0.74 57.4 111.84 6.48
51 78.4 0.79 57.9 112.64 6.58
52 80.0 0.85 58.5 113.6 6.70
53 81.0 0.88 58.8 114.08 6.76
54 82.3 0.93 59.3 114.88 6.86
55 83.2 0.96 59.6 115.36 6.92
56 84.5 1.02 60.2 116.32 7.04
57 85.3 1.05 60.5 116.68 7.10
58 86.5 1.1 61.00 117.6 7.20
59 88.1 1.18 61.8 118.88 7.36
60 88.9 1.22 62.2 119.52 7.44
61 90.3 1.30 62.3 120.8 7.60
62 91.7 1.38 63.8 122.08 7.76
63 93.1 1.48 64.8 123.68 7.96
64 94.7 1.62 66.2 125.92 8.24
65 95.6 1.69 66.9 127.04 83.8
66 96.7 1.84 68.4 129.44 8.68
67 97.8 2.02 70.2 132.32 9.04
68 98.4 2.15 71.50 134.40 9.30
69 98.8 2.26 72.60 136.16 9.52
70 99.0 2.33 73.30 137.28 9.66
71 99.4 2.51 75.10 140.16 10.02
72 99.7 2.75 77.50 144.00 10.50
73 99.8 2.88 78.8 146.08 10.76
75 99.9 2.96 79.6 147.36 10.92
77 100 3.00 80.0 148 11
Table 4–10: Row scores and their equivalent, Percentile Rank, z- scores, T- scores,
Deviation Intelligence Quotient (DIQ), and Stanine for Tenth (X) grade
Raw- Percentile z- scores T- scores DIQ Stanine
94
scores Ranks
12 0.1 -3.0 20 52 -1
15 1.0 -2.33 26.7 62.72 0.34
16 2.2 -2.02 29.8 67.68 0.96
17 3.1 -1.87 31.30 70.08 1.26
18 5.0 -1.64 33.6 73.76 1.72
19 7.6 -1.43 35.7 77.12 2.14
20 11.4 -1.21 37.9 80.64 2.58
21 14.2 -1.07 39.3 82.88 2.86
22 16.7 -0.96 40.40 84.64 3.00
23 18.2 -0.91 40.9 85.44 3.81
24 20.1 -0.84 41.6 86.56 3.32
25 24.5 -0.69 43.1 88.96 3.62
26 29.3 -0.55 44.5 91.2 3.90
27 34.2 -0.41 45.9 93.44 4.18
28 36.7 -0.34 46.6 94.56 4.32
29 38.3 -0.30 47 95.20 4.40
30 39.7 -0.26 47.40 95.84 4.48
31 44.9 -0.13 48.7 97.92 4.74
32 49.7 -0.01 49.99 99.84 4.98
33 56.0 0.14 51.4 102.24 5.28
34 57.6 0.20 52 103.2 5.40
35 63.8 0.35 53.5 105.6 5.70
36 69.5 0.51 55.10 108.16 6.02
37 71.7 0.57 55.7 109.12 6.14
38 73.2 0.62 56.2 109.92 6.24
Table: 4–10 Continued.
Raw-
scores
Percentile
ranks
z- scores T- scores DIQ Stanine
95
39 75.8 0.70 57 111.2 6.40
40 78.6 0.79 57.9 112.64 6.58
41 80.5 0.86 58.6 113.76 6.72
42 82.0 0.92 59.2 114.72 6.84
43 83.9 0.99 59.9 115.84 6.98
44 85.5 1.06 60.6 116.96 7.12
45 87.4 1.15 61.5 118.4 7.30
46 88.1 1.18 61.8 118.88 7.36
47 89.9 1.28 62.8 120.48 7.56
48 91.1 1.35 63.50 121.16 7.70
49 92.4 1.43 64.3 122.88 7.86
50 93.5 1.51 65.1 124.16 8.02
51 94.7 1.62 66.2 125.92 8.24
52 95.7 1.72 67.2 127.52 8.44
53 96.0 1.76 67.6 128.16 8.52
54 96.9 1.87 68.7 129.92 8.74
55 97.4 1.95 69.50 131.2 8.90
56 98.1 2.07 70.7 133.12 9.14
57 98.4 2.15 71.5 134.4 9.30
58 99.0 2.32 73.2 137.12 9.64.
59 99.1 2.37 73.70 137.92 9.74
61 99.4 2.51 75.10 140.16 10.02
62 99.7 2.75 77.50 144 10.50
63 99.9 2.96 79.6 147.36 10.92
69 100 3.00 80 148 11
Table 4–11: Raw scores and their equivalent, Percentile Rank, Z- scores, T- scores,
Deviation Intelligence Quotient (DIQ), and Stanine for Eleventh (XI) Grade.
Raw- Percentile z- scores T- scores DIQ Stanine
96
scores Ranks
17 0.2 -3.0 20 52 -1
18 0.6 -2.51 24.9 59.84 -0.02
19 1.5 -2.17 28.3 65.28 .66
20 2.8 -1.91 30.9 69.44 1.18
21 6.2 -1.54 34.6 75.36 1.92
22 8.2 -1.39 36.1 77.76 2.22
23 9.0 -1.35 36.5 78.4 2.30
24 10.1 -1.28 37.2 79.52 2.44
25 12.7 -1.14 38.6 81.76 2.72
26 14.6 -1.05 39.5 83.20 2.90
27 16.5 -0.97 40.3 84.48 3.06
28 18.2 -0.91 40.9 85.44 3.18
29 19.7 -0.86 41.4 86.24 3.28
30 21.7 -0.78 42.2 87.52 3.44
31 26.2 -0.64 43.6 89.76 3.72
32 30.7 -0.50 45 92.00 4.00
33 35.8 -0.36 46.4 94.24 4.28
34 37.1 -0.33 46.7 94.72 4.34
35 40.1 -0.25 48.5 96 4.50
36 45.5 -0.12 48.8 98.08 4.76
37 49.1 -0.03 49.7 99.52 4.94
38 53.6 +0.16 51.6 102.56 5.32
39 57.1 +0.18 51.8 102.88 5.36
40 60.1 0.26 52.6 104.16 5.52
41 61.2 0.29 52.9 104.64 5.58
Table 4–11: Continued.
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
97
42 63.3 0.34 53.4 105.44 5.68
43 65.9 0.41 54.1 106.56 5.82
44 67.6 0.46 54.6 407.36 5.92
45 70.2 0.53 55.3 108.48 6.06
46 71.2 0.56 55.6 108.96 6.12
47 72.7 0.60 56.0 109.6 6.20
48 74.0 0.65 56.5 110.4 6.30
49 74.7 0.67 56.7 110.72 6.34
50 76.6 0.73 57.3 111.68 6.46
51 78.3 0.79 57.9 112.64 6.58
52 79.8 0.83 58.3 113.28 6.66
53 80.7 0.87 58.7 113.92 6.74
54 81.8 0.91 59.1 114.56 6.82
55 82.8 0.95 59.5 115.2 6.90
56 83.3 0.97 59.7 115.52 6.64
57 84.3 1.01 60.1 116.16 7.02
58 85.6 1.07 60.7 117.12 7.14
59 88.2 1.19 61.9 119.04 7.38
60 88.6 1.21 62.1 119.36 7.42
61 89.9 1.27 62.7 120.32 7.54
62 91.0 1.34 63.4 121.44 7.68
63 92.3 1.43 64.3 122.88 7.86
64 94.2 1.57 65.7 125.12 8.14
65 95.3 1.67 66.7 126.72 8.34
66 96.1 1.76 67.6 128.16 8.52
67 97.6 1.97 69.7 131.52 8.94
Table 4–11: Continued.
98
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
68 98.3 2.12 71.2 133.92 9.24
69 98.9 2.29 72.9 136.64 9.58
70 99.1 2.35 73.5 137.6 9.70
71 99.8 2.88 78.8 146.08 10.76
72 100 3.00 80.0 148 11
Table 4–12: Row scores and their equivalent, Percentile Rank, z- scores, T-
scores, Deviation Intelligence Quotient (DIQ), and Stanine for Twelfth (XII) Grade
Raw-
scores
Percentile
ranks
z- scores T- scores DIQ Stanine
19 0.2 -2.88 21.2 53.92 -0.76
21 0.5 -2.60 24 58.40 0.20
22 1.5 -2.33 26.7 62.72 .34
23 1.2 -2.26 27.4 63.84 0.48
24 1.7 -2.12 28.8 66.08 0.76
25 2.2 -2.01 29.9 67.84 0.98
26 3.9 -1.76 32.4 71.84 1.48
27 4.8 -1.66 33.4 73.44 1.68
28 5.1 -1.64 33.6 73.76 1.72
29 5.8 -1.57 34.3 74.88 1.86
30 6.5 -1.50 35.0 76.00 2.00
31 9.7 -1.30 37.0 79.2 2.40
32 11.1 -1.22 37.8 80.48 2.56
33 14.5 -1.06 39.4 83.04 2.88
Table 4–12: Continued.
99
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
34 15.0 -1.03 39.7 83.52 2.94
35 16.7 -0.97 40.3 84.48 3.06
36 19.4 -0.86 41.4 86.24 3.28
37 20.6 -0.82 41.8 86.88 3.36
38 22.0 -0.76 42.4 87.84 3.42
39 25.2 -0.67 43.4 89.28 3.66
40 27.8 -0.59 44.1 90.56 3.82
41 31.0 -0.49 45.1 92.16 4.02
42 32.2 -0.47 45.3 92.48 4.06
43 35.8 -0.37 46.3 94.08 4.26
44 38.7 -0.29 47.1 95.36 4.42
45 41.9 -0.21 47.9 96.64 4.58
46 43.1 -0.18 48.2 97.12 4.64
47 44.6 -0.14 48.6 97.76 4.72
48 46.7 -0.08 49.2 98.72 4.84
49 48.2 -0.05 49.5 99.2 4.90
50 49.6 -0.01 49.9 99.84 4.98
51 51.6 0.04 50.40 100.64 5.08
52 54.2 0.10 51.0 101.6 5.20
53 56.7 0.17 51.7 102.72 5.34
54 58.8 0.22 52.2 103.52 5.44
55 60.3 0.26 52.6 104.16 5.52
56 63.4 0.34 53.4 105.44 5.68
57 64.6 0.38 53.8 106.08 5.76
58 67.1 0.45 54.5 107.2 5.90
Table 4–12: Continued
100
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
59 69.7 0.52 55.2 108.32 6.04
60 72.2 0.59 55.9 109.44 6.18
61 75.8 0.70 57.0 111.2 6.40
62 79.4 0.82 58.2 113.12 6.64
63 82.8 0.95 59.5 115.2 6.90
64 86.7 1.16 61.6 118.56 7.32
65 89.1 1.23 62.3 119.68 7.46
66 92.0 1.40 64.0 122.4 7.80
67 94.7 1.62 66.2 125.92 8.24
68 96.1 1.76 67.6 128.16 8.52
69 96.6 1.82 68.2 129.12 8.64
70 97.3 1.92 69.2 130.72 8.84
71 98.1 2.07 70.7 133.12 9.14
72 98.8 2.25 72.5 136.00 9.50
73 99.3 2.45 74.5 139.2 9.90
75 99.5 2.57 75.7 141.12 10.14
77 100 3.00 80.0 148 11
101
Table 4–13: Row scores and their equivalent, Percentile Rank, z- scores, T- scores,
Deviation Intelligence Quotient (DIQ), and Stanine for Age 15.
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
15 0.6 -2.51 24.9 59.84 -0.02
16 3.5 -1.81 31.9 71.04 1.38
17 4.2 -1.73 32.7 72.32 1.54
18 6.1 -1.55 34.5 75.2 1.9
19 9.3 -1.32 36.8 78.88 2.36
20 14.1 -1.08 39.2 82.22 2.84
21 17.9 -0.85 41.5 86.4 3.3
22 21.5 -0.79 42.1 87.36 3.42
23 23.4 -0.73 42.7 88.32 3.54
24 25.6 -0.66 43.4 89.44 3.68
25 30.1 -0.52 44.8 91.68 3.96
26 34.9 -0.39 46.10 93.76 4.22
27 39.7 -0.29 47.40 95.84 4.48
28 42.0 -0.20 48 96.8 4.6
29 42.6 -0.19 48.1 96.96 4.62
30 43.6 -0.16 48.40 97.44 4.68
31 49.7 -0.01 49.9 99.84 4.98
32 55.8 +0.15 51.5 102.4 5.3
33 59.6 0.24 52.40 103.84 5.48
34 60.3 0.26 52.60 104.16 5.52
35 64.4 0.37 53.7 105.92 5.74
36 70.5 0.54 55.4 108.64 6.08
37 72.1 0.59 55.9 109.44 6.18
38 73.7 0.64 56.40 110.24 6.28
39 76.3 0.72 57.2 111.52 6.44
102
Table 4–13: Continued
Raw-
scores
Percentile
ranks
z- scores T- scores DIQ Stanine
40 81.4 0.90 59.0 114.4 6.8
41 82.4 0.93 59.3 114.88 6.86
42 84.0 1.00 60.0 116 7.00
43 87.2 1.14 61.40 118.24 7.28
44 88.1 1.18 61.80 118.88 7.36
45 90.4 1.31 63.10 120.96 7.62
47 92.9 1.47 64.7 123.52 7.94
48 94.2 1.58 65.8 125.28 8.16
49 95.5 1.70 67.0 127.2 8.4
50 97.4 1.95 69.5 131.2 8.9
52 98.1 2.08 70.8 133.28 9.16
54 98.4 2.12 71.2 133.92 9.24
57 98.7 2.23 72.30 135.68 9.46
58 99.0 2.33 73.30 137.28 9.66
59 99.4 2.51 75.10 140.16 10.02
62 99.7 2.75 77.5 144 10.50
71 100 3.00 80.00 148 11
Table 4–14: Row scores and their equivalent, Percentile Rank, z- scores, T- scores,
Deviation Intelligence Quotient (DIQ), and Stanine for Age 16.
103
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
12 0.3 -2.75 22.5 56 0.5
15 0.5 -2.58 24.2 58.72 0.16
17 1.8 -2.1 29 66.40 0.80
18 3.4 -1.83 31.70 70.72 1.34
19 6.5 -1.51 34.90 75.84 1.98
20 8.8 -1.35 36.50 78.40 2.30
21 11.4 -0.1.21 37.90 80.64 2.58
22 12.5 -1.15 38.50 81.60 2.70
23 13.5 -1.1 39.00 82.40 2.80
24 16.1 -0.99 40.1 84.16 3.02
25 20.0 -0.84 41.6 86.56 3.32
26 23.9 -0.71 42.90 88.64 3.58
27 27.3 -0.60 44 90.4 3.80
28 29.4 -0.55 44.5 91.2 3.90
29 30.9 -0.49 45.1 92.16 4.02
30 33.0 -0.44 45.6 92.96 4.12
31 37.1 -0.33 46.7 94.72 4.34
32 40.8 -0.24 47.6 96.16 4.52
33 48.3 -0.04 49.6 99.36 4.92
34 50.1 +0.01 50.1 100.10 5.02
35 56.1 +0.16 51.6 102.56 5.32
36 62.1 0.31 53.1 104.96 5.62
37 64.7 0.38 53.8 106.08 5.76
38 67.3 0.45 54.5 107.20 5.90
39 70.9 0.55 55.5 108.80 6.10
Table 4–14: Continued
104
Raw-
scores
Percentile
Ranks
z- scores T- scores DIQ Stanine
40 72.5 0.60 56.00 109.60 6.20
41 74.8 0.67 56.70 110.72 6.34
42 75.1 0.68 56.80 110.88 6.36
43 76.9 0.73 57.30 111.68 6.46
44 79.2 0.82 58.20 113.12 6.64
45 80.8 0.87 58.70 113.92 6.74
46 81.6 0.90 59.00 114.4 6.80
47 82.9 0.95 59.50 115.2 6.90
48 84.4 1.01 60.10 116.16 7.02
49 85.5 1.06 60.60 116.96 7.12
50 86.8 1.12 61.2 117.92 7.24
51 88.8 1.22 62.2 119.52 7.44
52 90.9 1.34 63.4 121.44 7.68
53 91.7 1.39 63.9 122.24 7.78
54 93.2 1.49 64.9 123.84 7.98
55 93.8 1.54 65.4 124.64 8.08
56 95.1 1.65 66.50 126.4 8.30
57 95.3 1.67 66.70 126.72 8.34
58 95.8 1.73 67.30 127.68 8.46
59 96.4 1.80 68.00 128.8 8.60
60 96.9 1.87 68.70 129.92 8.74
61 97.9 2.04 70.40 132.64 9.08
62 98.4 2.15 71.50 134.4 9.30
64 99.2 2.41 74.10 138.55 9.82
67 99.5 1.58 65.80 125.28 8.16
68 99.7 2.75 77.50 144 10.50
69 100 3.00 80.00 148 11
105
Table 4–15: Row scores and their equivalent, Percentile Rank, z- scores, T- scores,
Deviation Intelligence Quotient (DIQ), and Stanine for Age 17.
Raw- scores Percentile ranks z- scores T- scores DIQ Stanine
18 0.3 -2.75 22.5 56 -0.5
20 0.8 -2.41 25.9 61.44 0.18
21 2.3 -2.00 30.0 68.0 1
22 3.4 -1.83 31.7 70.72 1.34
23 3.7 -1.79 32.1 71.36 1.42
24 4.2 -1.73 32.7 72.32 1.54
25 6.5 -1.52 34.8 75.68 1.96
26 9.3 -1.32 36.8 78.88 2.36
27 11.3 -1.21 37.9 80.64 2.58
28 13.6 -1.10 39.00 82.4 2.8
29 16.4 -0.98 40.2 84.32 3.04
30 18.9 -0.88 41.2 85.92 3.24
31 23.4 -0.73 42.7 88.32 3.54
32 26.3 -0.64 43.6 89.76 3.72
33 31.1 -0.52 44.8 91.68 3.96
34 32.5 -0.45 45.5 92.8 4.1
35 37.3 -0.33 46.7 94.72 4.34
36 41.0 -0.23 47.7 96.32 4.54
37 44.4 -0.14 48.6 97.79 4.72
38 47.5 -0.06 49.4 99.04 4.88
39 51.7 +0.04 50.4 100.64 5.08
40 54.2 +0.11 51.1 101.76 5.22
41 57.6 0.19 51.9 103.04 5.38
42 61.3 0.29 52.9 104.64 5.58
43 63.3 0.33 53.3 105.28 5.66
106
Table 4–15: Continued
Raw- scores Percentile ranks z- scores T- scores DIQ Stanine
44 65.8 0.41 54.1 106.56 5.82
45 69.2 0.50 55.0 108.0 6.00
46 71.5 0.57 55.7 109.12 6.14
47 73.4 0.63 56.3 110.08 6.26
48 74.9 0.68 56.8 110.88 6.36
49 76.0 0.71 57.1 111.36 6.42
50 77.7 0.76 57.6 112.16 6.52
51 79.7 0.83 58.3 113.28 6.66
52 81.6 0.90 59.0 114.4 6.8
53 82.9 0.91 59.10 114.56 6.82
54 83.6 0.98 59.8 115.68 6.96
55 84.7 1.03 60.3 116.48 7.06
56 85.3 1.05 60.5 116.8 7.10
57 86.7 1.11 61.1 117.76 7.22
58 88.1 1.18 61.8 118.88 7.36
59 90.1 1.29 62.9 120.64 7.58
60 91.2 1.35 63.5 121.6 7.75
61 92.4 1.43 64.3 122.88 7.86
62 93.8 1.54 65.4 124.64 8.08
63 94.9 1.64 66.4 126.24 8.28
64 96.3 1.79 67.9 128.64 8.58
65 97.5 1.96 69.6 131.36 8.92
66 97.7 2.00 70.0 132 9.0
67 98.9 2.29 72.9 136.64 9.58
68 99.4 2.54 75.1 140.16 10.02
69 99.7 2.75 77.5 144 10.5
72 100 3.00 80.00 148 11
107
Table 4–16: Row scores and their equivalent, Percentile Rank, z- scores, T- scores,
Deviation Intelligence Quotient (DIQ), and Stanine for Age 18.
Raw- scores Percentile ranks z- scores T- scores DIQ Stanine
16 0.6 -2.51 24.9 59.84 0.02
18 1.3 -2.23 27.7 64.32 0.54
19 1.6 -2.15 28.5 65.69 0.70
20 2.2 -2.02 29.8 67.68 0.96
21 4.4 -1.71 32.9 72.64 1.58
22 5.9 -1.57 34.3 74.88 1.86
23 6.9 -1.48 35.2 76.32 2.04
25 8.8 -1.35 36.5 78.4 2.3
26 10.9 -1.23 37.7 80.32 2.54
27 13.1 -1.12 38.8 82.8 2.70
28 13.4 -1.11 38.9 82.24 2.78
29 14.4 -1.07 39.3 82.88 2.86
30 15.0 -1.04 39.6 83.36 2.92
31 19.4 -0.87 41.3 86.08 3.26
32 22.2 -0.77 42.3 87.68 3.46
33 27.2 -0.60 44.0 90.40 3.80
34 28.1 -0.55 44.5 91.2 3.90
35 30.3 -0.52 44.8 91.68 3.96
36 34.1 -0.41 45.9 93.44 4.18
37 35.9 -0.36 46.4 97.24 4.28
38 38.1 -0.30 47.00 95.20 4.40
39 40.0 -0.26 47.40 95.84 4.48
40 41.9 -0.22 47.80 96.48 4.56
41 42.8 -0.20 48.00 96.80 4.60
42 43.8 -0.16 48.40 97.44 4.68
43 47.8 -0.06 49.40 99.04 4.88
108
Table 4–16: Continued.
Raw- scores Percentile ranks z- scores T- scores DIQ Stanine
44 49.4 -0.02 49.80 99.68 4.96
45 51.6 +0.04 50.40 100.64 5.08
46 52.5 0.07 50.70 101.12 5.14
47 53.8 0.10 51.0 101.6 5.20
48 55.6 0.14 51.40 102.14 5.28
49 56.6 0.17 51.70 102.72 5.34
50 57.8 0.20 52.0 103.20 5.40
51 59.4 0.24 52.4 103.68 5.48
52 60.9 0.28 52.80 104.48 5.56
53 63.1 0.34 53.40 105.44 5.68
54 64.4 0.37 53.70 105.92 5.74
55 65.9 0.41 54.10 106.56 5.82
56 68.4 0.48 54.80 107.68 5.96
57 69.4 0.51 55.10 108.16 6.02
58 71.9 0.58 55.8 109.28 6.16
59 73.4 0.63 56.30 110.08 6.26
60 74.4 0.66 56.60 110.56 6.32
61 76.9 0.74 57.40 111.84 6.48
62 79.7 0.83 58.30 113.28 6.66
63 83.4 0.97 59.70 115.52 6.94
64 86.6 1.11 61.1 117.76 7.22
65 89.1 1.23 62.3 119.68 7.46
66 92.2 1.42 64.2 122.72 7.84
109
Table 4–16: Continued
Raw- scores Percentile ranks z- scores T- scores DIQ Stanine
67 95.6 1.71 67.1 127.36 8.42
68 96.3 1.79 67.9 128.64 8.58
69 97.5 1.96 69.6 131.36 8.92
70 98.1 2.08 70.8 133.28 9.16
71 98.4 2.15 71.50 134.4 9.30
72 98.8 2.26 72.60 136.16 9.52
73 99.4 2.51 75.10 140.16 10.02
75 99.7 2.75 77.5 144 10.5
77 100 3.00 80.00 148 11
Table 4–17: Row scores and their equivalent, Percentile Rank, z- scores, T-
scores, Deviation Intelligence Quotient (DIQ), and Stanine for Age 19.
Raw- scores Percentile ranks z- scores T- scores DIQ Stanine
20 2.1 -2.04 29.6 67.36 0.92
21 3.2 -1.86 31.4 70.24 1.28
22 5.3 -1.62 33.8 74.08 1.76
23 5.8 -1.57 34.30 74.88 1.86
24 6.3 -1.53 34.70 75.52 1.94
25 6.8 -1.49 35.10 76.16 2.02
26 7.9 -1.41 35.90 77.44 2.18
27 10.0 -1.29 37.10 79.36 2.42
28 11.1 -1.22 37.80 80.48 2.56
31 13.2 -1.07 39.30 82.88 2.86
32 17.4 -0.94 40.6 84.96 3.12
33 21.1 -0.81 41.9 87.04 3.38
34 22.1 -0.77 42.30 87.68 3.46
110
Table 4–17: Continued
Raw- scores Percentile
Ranks
z- scores T- scores DIQ Stanine
35 23.7 -0.72 42.8 88.48 3.56
36 27.9 -0.56 44.4 91.04 3.88
38 32.1 -0.44 45.6 92.96 4.12
39 34.2 -0.39 46.1 94.24 4.22
40 37.9 -0.31 46.9 95.04 4.38
41 40.0 -0.26 47.4 95.84 4.48
42 41.6 -0.22 48.8 96.48 4.56
43 43.2 -0.18 48.2 97.12 4.64
44 45.8 -0.11 48.9 98.24 4.78
45 48.9 -0.03 49.7 99.52 4.94
46 49.5 -0.02 49.8 99.68 4.96
47 50.0 .000 50 100 5
48 51.1 +0.03 50.3 100.48 5.06
49 52.6 0.07 50.3 100.48 5.06
50 53.7 0.10 51.0 101.16 5.20
51 55.6 0.14 51.40 102.24 5.28
52 57.4 0.19 51.90 103.04 5.38
53 60.0 0.27 52.7 104.32 5.54
54 61.6 0.30 53.0 104.8 5.60
55 63.2 0.34 53.4 105.44 5.68
56 65.8 0.41 54.10 106.56 5.82
57 66.8 0.44 54.4 107.04 5.88
58 68.9 0.52 55.2 108.32 6.04
59 73.7 0.64 56.4 110.24 6.28
60 75.3 0.69 56.9 111.04 6.38
111
Table 4–17: Continued
Raw- scores Percentile
Ranks
z- scores T- scores DIQ Stanine
61 78.9 0.80 58.0 112.80 6.60
62 81.6 0.90 59.0 114.4 6.80
63 84.2 1.01 60.1 116.16 7.02
64 87.9 1.17 61.7 118.72 7.34
65 89.5 1.26 62.6 120.16 7.52
66 92.1 1.41 64.1 122.56 7.82
67 63.2 1.50 65.0 124 8.00
68 95.3 1.67 66.7 126.72 8.34
70 96.3 1.79 67.9 128.64 8.58
71 98.4 2.15 71.5 134.4 9.30
72 99.5 2.58 75.8 141.28 10.16
77 100 3.00 80.00 148 11
112