A Study into the performance of grade 10 pupils

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There are descriptive analyses the performance of grade 10 students in XYZ College in this assignment. XYZ college administration would like to examine the performance of grade 10 classes. Therefore they collected the marks for the science subject in each class.

Such that school administration has decided that, best 10% of the students should be awarded a merit certificate and worst 10% of the students should be attended for extra classes.

A group of 6 students are selected for a quiz program related to the science subject. Exclude the class that shows the worst performance based on analyzing each class and select two students from other three classes.

Following are those data.

In XYZ College, there are four classes of grade 10(A, B, C, D).Following is the marks for the science subject for the year and examination.

A

B

C

D

47

58

54

58

51

68

55

59

74

39

26

52

64

54

51

50

78

64

61

41

87

40

51

67

44

65

71

49

62

56

71

42

37

56

52

41

61

55

51

52

36

65

46

50

67

60

47

36

52

27

47

36

31

52

67

72

57

64

54

29

52

42

52

35

25

34

41

47

52

37

36

46

73

59

57

42

63

79

56

50

56

70

35

44

59

66

67

33

62

63

57

41

68

75

52

50

31

70

49

52

48

51

76

50

83

73

58

57

55

89

29

70

60

92

52

53

52

53

60

64

66

52

43

47

55

71

64

48

Methodology

We can describe the data analysis using graphical illustrations,

Bar charts

Simple bar chart

Pie chart

Stem and leaf plot

Stem

Leaves

2

3

4

5

6

2,4

4,6,8,8,9

0,1,3,5,7,8

5,7,

2,4,5,6,8

Histogram

Percentiles

Consider the above stem and leaf,

The position of Rth percentile =R Ã- 20/100

Probability

Multiplication Rule

If an event can occur in m ways and another event can occur in n ways and if the two events cannot occur simultaneously, the one of the two event can occur in m+ n ways.

Additional Rule

If an event can occur in m ways and the second event can occur in n ways and if the number of ways the second event occurs does not depend upon how the first event occurs then the two events can occur simultaneously in mn ways.

Students' performance of four classes

There are most student of class A and class B between 55 and 70 marks. Class A has a student higher than 85 marks. Class B has two students higher than 85 marks.

There are most students of class C and D between 40 and 55 marks. Class C and Class D have not students higher than 85 marks.

Stem

Leaves

2

3

4

5

6

7

8

5

1, 1, 6, 7

4, 7, 8

1, 2, 2, 2, 2, 5, 5, 6, 7, 9

0, 6, 8, 2, 3, 7, 1, 2, 4

3, 8, 4

3, 7

Marks of class A

Stem

Leaves

2

3

4

5

6

7

8

9

7

9, 4, 7

0, 2, 8

8, 4, 6, 6, 5, 2, 9, 1, 3, 2

8, 4, 5, 5, 0, 4, 6, 3

9, 0, 5, 0, 3, 1

9

2

Marks of class B

Marks of class C

Stem

leaves

2

3

4

5

6

7

6, 9

6, 5

6, 7, 7, 1, 9, 3

5, 5, 1, 1, 2, 1, 4, 2, 7, 6, 7, 2, 8, 2, 4

1, 7, 7, 0

1, 1, 6

Marks of class D

Stem

Leaves

2

3

4

5

6

7

9

6, 6, 5, 3

1, 9, 2, 1, 7, 6, 2, 4, 1, 7

8, 9, 2, 0, 2, 0, 0, 0, 2, 0, 7, 3

7, 4

2, 0

By above graphical analysis students of class B is better than other classes. Students of class A are as clever as students of class B. Students of class D are the weakest.

Classify for level

(The best 10% of the all students should be awarded = Total students Ã- 10%

a merit certificate) =128Ã-10%

=12.8

=13

{The worst 10% of the all students should be attended for =128 Ã- 10%

Extra classes} =12.8

=13

Five students of class A award merit certificates. Six students of class B and three students of class C award merit certificates. Only one student of class D awards a merit certificate.

Five students of class A, two students of class B, five students of class C and five students of class D attend for extra class.

Possible group for a quiz program

A group of 6 students are selected for a quiz program related to the science subject. Exclude the class D and select two students from other three classes. Two students selected randomly from the three students who obtained the highest mark of each class.

A group of highest marks

A

B

C

87 - A1

92 - B1

76 - C1

83 - A2

89 - B2

71 - C2

78 - A3

79 - B3

71 - C3

The number of possible group of two students who are selected randomly = 3C2 = 3

from the three students of class A

The number of possible group of two students who are selected randomly = 3

From the three students of class B

The number of possible group of two students who are selected randomly = 3

From the three students of class C

Therefore the total number of possible groups = 3Ã-3Ã-3

= 27

Possible group of class A = {A1, A2}, {A1, A3}, {A2, A3}

Possible group of class B = {B1, B2}, {B1, B3}, {B2, B3}

Possible group of class C = {C1, C2}, {C1, C3}, {C2, C3}

A1 + A2 = 87 + 83 = 170 = a1

A1 + A3 = 87 + 78 = 165 = a2

A2 + A3 = 83 + 78 = 161 = a3

B1 + B2 = 92 + 89 = 181 = b1

B1 + B3 = 92 + 79 = 171 = b2

B2 + B3 = 89 + 79 = 168 = b3

C1 + C2 = 76 + 71 = 147 = c1

C1 + C2 = 76 + 71 = 147 = c2

C2 + C3 = 71 + 71 = 142 = c3

Values of possible group of 6 students

a1 + b1 + c1 = 498

a1 + b1 + c2 = 498

a1 + b1 + c3 = 493

a1 + b2 + c1 = 488

a1 + b2 + c2 = 488

a1 + b2 + c3 = 483

a1 + b3 + c1 = 485

a1 + b3 + c2 = 485

a1 + b3 + c3 = 480

a2 + b1 + c1 = 493

a2 + b1 + c2 = 493

a2 + b1 + c3 = 488

a2 + b2 + c1 = 483

a2 + b2 + c2 = 483

a2 + b2 + c3 = 478

a2 + b3 + c1 = 480

a2 + b3 + c2 = 480

a2 + b3 + c3 = 475

a3 + b1 + c1 = 489

a3 + b1 + c2 = 489

a3 + b1 + c3 = 484

a3 + b2 + c1 = 476

a3 + b2 + c2 = 476

a3 + b2 + c3 = 471

a3 1 + b3 + c1 = 476

a3 + b3 + c2 = 476

a3 + b3 + c3 = 471

A team total mark of the 6 students greater than 490 has a higher chance of winning the quiz, a team with the total mark of the 6 students between 475 and 490 has an average chance of winning and a team with the total mark less than 475 has a slight chance of winning.

Probability of forming a team with higher chance of winning = 5/27

Probability of forming a team with an average chance of winning = 20/27

Probability of forming a team with a slight chance of winning = 2/27

Suggestion

There are higher marks students in the A, B classes better than selected class C.

Example:-

Selected class C students marks :- 76, 71, 71

Not selected class A & B student's marks than selected class C :-

A :- 73, 74

B :-75, 73

Therefore nine students are selected from highest marks students from four classes more suitable than select from three classes. Then we can increase the probability of forming a team with higher chance of winning.