1 .Introduction

Analysis of the Ivy League Exam done by Standard 8 pupils at Ebulako Primary School in 2023. The students are divided into 3 streams namely Atlanta, Indianna and Pacifica. Each of the students sat 5 exams for the 5 compulsory subjects offered at the Primary school level. They are English, Kiswahili, Mathematics, Science and SSRE. (Social Studies and Religious Education) Each subject is marked out of 100 marks, therefore the maximum total mark a student can attain is 500 marks. A total of 179 students sat the exam and had their marks recorded and analysed below.

2. Class performance per subject

A. Atlanta

a. English

Here are the descriptive summaries of how students from Atlanta performed in English.

  25%
minimum 8
lower.quartile 43.75
Median 55
upper.quartile 64
maximum 78
average 53.45
standard.deviation 14.38
c.o.v 26.91

Distribution

The table below shows the percentage distribution of marks in English.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
2 0 4 15 22 24 24 12 0 0

A majority of the students in Atlanta attained a score ranging from 51 to 70.

Density function

Atlanta’s English scores have a kurtosis value of 3.19 and a skewness value of -0.59. This implies that the distribution is leptokurtic and is skewed negatively about the mean.

b. Kiswahili

Here are the descriptive summaries of how students from Atlanta performed in Kiswahili.

  25%
minimum 30
lower.q 53.75
Median 63
upper.q 70.25
maximum 83
average 61.07
standard.dev 13.03
c.o.v 21.34

Distribution

The table below shows the percentage distribution of marks in Kiswahili.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 2 9 10 25 30 20 5 0

A majority of the students in Atlanta attained a score ranging from 61 to 70.

Density function

Atlanta’s Kiswahili scores have a kurtosis value of 2.57 and a skewness value of -0.48. This implies that the distribution is platykurtic and is skewed negatively about the mean.

c. Mathematics

Here are the descriptive summaries of how students from Atlanta performed in Mathematics.

  25%
minimum 4
lower.q 33.5
Median 42
upper.q 54
maximum 88
average 44.7
standard.dev 18.13
c.o.v 40.57

Distribution

The table below shows the percentage distribution of marks in Mathematics.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
2 5 12 29 25 12 7 5 5 0

A majority of the students in Atlanta attained a score ranging from 31 to 40.

Density function

Atlanta’s Mathematics scores have a kurtosis value of 3.07 and a skewness value of 0.59. This implies that the distribution is leptokurtic and has a mild skewness about the mean.

d. Science

Here are the descriptive summaries of how students from Atlanta performed in Science.

  25%
minimum 32
lower.q 50
Median 60
upper.q 70.5
maximum 92
average 60.6
standard.dev 14.34
c.o.v 23.66

Distribution

The table below shows the percentage distribution of marks in Science.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 0 9 19 29 20 17 7 2

A majority of the students in Atlanta attained a score ranging from 51 to 60.

Density function

Atlanta’s Science scores have a kurtosis value of 2.45 and a skewness value of 0.08. This implies that the distribution is platykurtic and has a mild skewness about the mean.

e. SSRE

Here are the descriptive summaries of how students from Atlanta performed in SSRE.

  25%
minimum 28
lower.q 59.5
Median 69.5
upper.q 76
maximum 91
average 66.9
standard.dev 13.1
c.o.v 19.58

Distribution

The table below shows the percentage distribution of marks in SSRE.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 2 2 5 20 25 34 12 2

A majority of the students in Atlanta attained a score ranging from 71 to 80.

Density function

Atlanta’s SSRE scores have a kurtosis value of 3.2 and a skewness value of -0.69. This implies that the distribution is leptokurtic and has a negative skewness about the mean.

f. Total

Here are the descriptive summaries of how students from Atlanta performed in all the subjects.

  25%
minimum 136
lower.q 243.5
Median 288
upper.q 329
maximum 411
average 286.7
standard.dev 64.13
c.o.v 22.37

Distribution

The table below shows the percentage distribution of total marks in the Atlanta class.

0-100 101-200 201-300 301-400 401-500
0 10 50 35 5

A majority of the students in Atlanta attained a total score ranging from 201 to 300.

Density function

Atlanta’s total scores have a kurtosis value of 2.57 and a skewness value of -0.02. This implies that the distribution is platykurtic and has a mild skewness about the mean.

B. Indianna

a. English

Here are the descriptive summaries of how students from Indianna performed in English.

  25%
minimum 22
lower.q 46.75
Median 54.5
upper.q 61.75
maximum 84
average 53.67
standard.dev 12.51
c.o.v 23.31

Distribution

The table below shows the percentage distribution of marks in English.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 6 13 16 38 21 7 2 0

A majority of the students in Indianna attained a score ranging from 51 to 60.

Density function

Indianna’s English scores have a kurtosis value of 3.2 and a skewness value of -0.22. This implies that the distribution is leptokurtic and is mildly skewed about the mean.

b. Kiswahili

Here are the descriptive summaries of how students from Indianna performed in Kiswahili.

  25%
minimum 32
lower.q 52.75
Median 61
upper.q 67.75
maximum 79
average 59.78
standard.dev 11.67
c.o.v 19.52

Distribution

The table below shows the percentage distribution of marks in Kiswahili.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 0 9 9 32 37 16 0 0

A majority of the students in Indianna attained a score ranging from 61 to 70.

Density function

Indianna’s Kiswahili scores have a kurtosis value of 2.96 and a skewness value of -0.61. This implies that the distribution is platykurtic and is moderately skewed about the mean.

c. Mathematics

Here are the descriptive summaries of how students from Indianna performed in Mathematics.

  25%
minimum 12
lower.q 32.5
Median 42
upper.q 61
maximum 86
average 45.9
standard.dev 17.51
c.o.v 38.15

Distribution

The table below shows the percentage distribution of marks in Mathematics.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 4 19 26 19 7 16 9 2 0

A majority of the students in Indianna attained a score ranging from 31 to 40.

Density function

Indianna’s Mathematics scores have a kurtosis value of 2.3 and a skewness value of 0.51. This implies that the distribution is platykurtic and has a moderate skewness about the mean.

d. Science

Here are the descriptive summaries of how students from Indianna performed in Science.

  25%
minimum 36
lower.q 50
Median 61
upper.q 73
maximum 94
average 61.62
standard.dev 16.26
c.o.v 26.39

Distribution

The table below shows the percentage distribution of marks in Science.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 0 16 14 21 25 11 13 4

A majority of the students in Indianna attained a score ranging from 61 to 70.

Density function

Indianna’s Science scores have a kurtosis value of 2.18 and a skewness value of 0.24. This implies that the distribution is platykurtic and has a mild skewness about the mean.

e. SSRE

Here are the descriptive summaries of how students from Indianna performed in SSRE.

  25%
minimum 34
lower.q 57.5
Median 67
upper.q 78.25
maximum 92
average 66.59
standard.dev 13.96
c.o.v 20.97

Distribution

The table below shows the percentage distribution of marks in SSRE.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 0 7 7 16 32 21 16 4

A majority of the students in Indianna attained a score ranging from 61 to 70.

Density function

Indianna’s SSRE scores have a kurtosis value of 2.63 and a skewness value of -0.39. This implies that the distribution is platykurtic and has a mild skewness about the mean.

f. Total

Here are the descriptive summaries of how students from Atlanta performed in all the subjects

  25%
minimum 166
lower.q 243
Median 281
upper.q 328.5
maximum 422
average 287.6
standard.dev 63.11
c.o.v 21.95

Distribution

The table below shows the percentage distribution of total marks in the Atlanta class.

0-100 101-200 201-300 301-400 401-500
0 10 50 35 5

A majority of the students in Indianna attained a total score ranging from 201 to 300.

Density function

Indianna’s total scores have a kurtosis value of 2.3 and a skewness value of 0.03. This implies that the distribution is platykurtic and has a mild skewness about the mean.

C. Pacifica

a. English

Here are the descriptive summaries of how students from Pacifica performed in English.

  25%
minimum 22
lower.q 46.75
Median 54.5
upper.q 61.75
maximum 84
average 53.67
standard.dev 12.51
c.o.v 23.31

Distribution

The table below shows the percentage distribution of marks in English.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 5 9 23 22 40 4 0 0

A majority of the students in Pacifica attained a score ranging from 61 to 70.

Density function

Pacifica’s English scores have a kurtosis value of 2.45 and a skewness value of -0.6. This implies that the distribution is platykurtic and is moderately skewed about the mean.

b. Kiswahili

Here are the descriptive summaries of how students from Pacifica performed in Kiswahili.

  25%
minimum 38
lower.q 53
Median 63
upper.q 68
maximum 78
average 61.16
standard.dev 10.32
c.o.v 16.87

Distribution

The table below shows the percentage distribution of marks in Kiswahili.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 0 2 22 14 43 22 0 0

A majority of the students in Indianna attained a score ranging from 61 to 70.

Density function

Pacifica’s Kiswahili scores have a kurtosis value of 2.19 and a skewness value of -0.39. This implies that the distribution is platykurtic and is mildly skewed about the mean.

c. Mathematics

Here are the descriptive summaries of how students from Pacifica performed in Mathematics.

  25%
minimum 22
lower.q 34
Median 44
upper.q 54
maximum 90
average 47.11
standard.dev 17.42
c.o.v 36.98

Distribution

The table below shows the percentage distribution of marks in Mathematics.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 4 19 26 19 7 16 9 2 0

A majority of the students in Pacifica attained a score ranging from 31 to 40.

Density function

Pacifica’s Mathematics scores have a kurtosis value of 2.77 and a skewness value of 0.74. This implies that the distribution is platykurtic and has a moderate skewness about the mean.

d. Science

Here are the descriptive summaries of how students from Pacifica performed in Science.

  25%
minimum 28
lower.q 50
Median 58
upper.q 72
maximum 92
average 60.23
standard.dev 16.3
c.o.v 27.06

Distribution

The table below shows the percentage distribution of marks in Science.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 4 10 15 27 20 12 14 2

A majority of the students in Pacifica attained a score ranging from 51 to 60 .

Density function

Pacifica’s Science scores have a kurtosis value of 2.25 and a skewness value of -0.03. This implies that the distribution is platykurtic and has a mild skewness about the mean.

e. SSRE

Here are the descriptive summaries of how students from Pacifica performed in SSRE.

  25%
minimum 40
lower.q 60
Median 67
upper.q 77
maximum 87
average 66.98
standard.dev 12.06
c.o.v 18.01

Distribution

The table below shows the percentage distribution of marks in SSRE.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 0 2 10 22 30 22 17 0

A majority of the students in Pacifica attained a score ranging from 61 to 70.

Density function

Pacifica’s SSRE scores have a kurtosis value of 2.06 and a skewness value of -0.22. This implies that the distribution is platykurtic and has a mild skewness about the mean.

f. Total

Here are the descriptive summaries of how students from Pacifica performed in all the subjects

  25%
minimum 163
lower.q 249
Median 296
upper.q 332
maximum 414
average 290.6
standard.dev 61.04
c.o.v 21.01

Distribution

The table below shows the percentage distribution of total marks in the Pacifica class.

0-100 101-200 201-300 301-400 401-500
0 9 46 45 2

A majority of the students in Pacifica attained a total score ranging from 201 to 300.

Density function

Pacifica’s total scores have a kurtosis value of 2.2 and a skewness value of -0.03. This implies that the distribution is platykurtic and has a mild skewness about the mean.

3. Combined performance

A. English

Here are the descriptive summaries of how all the students performed in English.

  25%
minimum 8
lower.q 45.5
Median 55
upper.q 64
maximum 84
average 54.08
standard.dev 13
c.o.v 24.04

Distribution

The table below shows the percentage distribution of marks in English.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
1 0 5 12 21 28 28 8 1 0

A majority of the students attained a score ranging from 51 to 70.

Density function

The combined English scores have a kurtosis value of 3.08 and a skewness value of -0.51. This implies that the distribution is leptokurtic and is moderately skewed about the mean.

B. Kiswahili

Here are the descriptive summaries of how all the students performed in Kiswahili.

  25%
minimum 30
lower.q 53
Median 63
upper.q 69.5
maximum 83
average 60.68
standard.dev 11.67
c.o.v 19.23

Distribution

The table below shows the percentage distribution of marks in Kiswahili.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 1 7 14 23 37 19 2 0

A majority of the students attained a score ranging from 61 to 70.

Density function

The combined Kiswahili scores have a kurtosis value of 2.73 and a skewness value of -0.51. This implies that the distribution is platykurtic and is moderately skewed about the mean.

C. Mathematics

Here are the descriptive summaries of how all the students performed in Mathematics.

  25%
minimum 4
lower.q 34
Median 42
upper.q 54
maximum 90
average 45.91
standard.dev 17.62
c.o.v 38.38

Distribution

The table below shows the percentage distribution of marks in Mathematics.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
1 3 17 27 22 11 10 8 4 0

A majority of the students attained a score ranging from 31 to 40.

Density function

The combined Mathematics scores have a kurtosis value of 2.75 and a skewness value of 0.6. This implies that the distribution is platykurtic and is moderately skewed about the mean.

D. Science

Here are the descriptive summaries of how all the students performed in Science.

  25%
minimum 28
lower.q 50
Median 60
upper.q 72
maximum 94
average 60.8
standard.dev 15.58
c.o.v 25.62

Distribution

The table below shows the percentage distribution of marks in Science.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 2 12 16 26 22 13 11 3

A majority of the students attained a score ranging from 51 to 60.

Density function

The combined Science scores have a kurtosis value of 2.32 and a skewness value of 0.1. This implies that the distribution is platykurtic and is mildly skewed about the mean.

E. SSRE

Here are the descriptive summaries of how all the students performed in SSRE.

  25%
minimum 28
lower.q 58.5
Median 68
upper.q 77
maximum 92
average 66.83
standard.dev 12.98
c.o.v 19.42

Distribution

The table below shows the percentage distribution of marks in SSRE.

0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100
0 0 1 4 8 19 29 26 15 2

A majority of the students attained a score ranging from 61 to 70.

Density function

The combined SSRE scores have a kurtosis value of 2.72 and a skewness value of -0.45. This implies that the distribution is platykurtic and is mildly skewed about the mean.

F. Total

Here are the descriptive summaries of how all the students in Ebulako Primary School performed in the 2023 Ivy League exam.

  25%
minimum 136
lower.q 244.5
Median 290
upper.q 330.5
maximum 422
average 288.3
standard.dev 62.43
c.o.v 21.65

Distribution

The table below shows the percentage distribution of the total marks.

0-100 101-200 201-300 301-400 401-500
0 10 47 41 4

A majority of the students attained a score ranging from 201 to 300.

Density function

The combined total scores have a kurtosis value of 2.37 and a skewness value of -0.01. This implies that the distribution is platykurtic and is mildly skewed about the mean.

4. Best students

The students who achieved the highest marks per subject are highlighted below.

English

english kiswahili math science SSRE stream total
84 72 86 94 86 I 422

Kiswahili

  english kiswahili math science SSRE stream total
5 71 83 84 92 81 A 411

Mathematics

  english kiswahili math science SSRE stream total
9 66 76 90 80 83 P 395

Science

  english kiswahili math science SSRE stream total
1 84 72 86 94 86 I 422
10 72 65 78 94 82 I 391

SSRE

  english kiswahili math science SSRE stream total
6 72 74 80 90 92 I 408

Total

english kiswahili math science SSRE stream total
84 72 86 94 86 I 422

5. Subject performance per class

A. English

a. Average

The mean scores for English from the 3 classes are shown below.

stream subject.mean
P 55.08
I 53.67
A 53.45

Leading in English is Pacifica with a mean score of 55.08, followed by Indianna then Atlanta.

b. Deviation

stream subject.sd
A 14.38
I 12.51
P 12.16

Atlanta recorded the highest deviation in English with 14.38 marks.

B. Kiswahili

a. Average

The mean scores for Kiswahili from the 3 classes are shown below.

stream subject.mean
P 61.16
A 61.07
I 59.78

Leading in Kiswahili is Pacifica with a mean score of 61.16, followed by Atlanta then Indianna.

b. Deviation

stream subject.sd
A 13.03
I 11.67
P 10.32

Atlanta recorded the highest deviation in Kiswahili with 13.03 marks.

C. Mathematics

a.Average

The mean scores for Mathematics from the 3 classes are shown below.

stream subject.mean
P 47.11
I 45.9
A 44.7

In Mathematics, Pacifica leads with a mean score of 47.11, followed by Indianna then Atlanta.

b. Deviation

stream subject.sd
A 18.13
I 17.51
P 17.42

Atlanta recorded the highest deviation in Mathematics with 18.13 marks.

D. Science

a. Average

The mean scores for Science from the 3 classes are shown below.

stream subject.mean
I 61.62
A 60.6
P 60.23

Leading in Science is Indianna with a mean score of 61.62, followed by Atlanta then Pacifica.

b. Deviation

stream subject.sd
P 16.3
I 16.26
A 14.34

Pacifica recorded the highest deviation in Science with 16.3 marks.

E. SSRE

a. Average

The mean scores for SSRE from the 3 classes are shown below.

stream subject.mean
P 66.98
A 66.9
I 66.59

In SSRE, Pacifica leads with a mean score of 66.98, followed by Atlanta then Pacifica.

b. Deviation

stream subject.sd
I 13.96
A 13.1
P 12.06

Indianna recorded the highest deviation in SSRE with 13.96 marks.

F. Total

a. Average

The overall mean scores for all the 3 classes are shown below.

stream subject.mean
P 290.6
I 287.6
A 286.7

Overally, Pacifica leads with an average score of 290.6 followed by Indianna then Atlanta.

b. Deviation

stream subject.sd
A 64.13
I 63.11
P 61.04

Atlanta recorded the highest overall score deviation with 64.13 marks.