A)  Test Analysis (Model 1)
Date of a test of general knowledge with 30 objective type items administered to a sample of 50 students.  The Answer Key for each item is given in the top.

Key

D

A

D

C

C

D

B

D

A

A

C

B

C

C

C

C

C

B

C

C

B

C

A

C

C

D

D

C

D

C

Q.No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

RollNo.

1

D

B

B

A

D

A

A

D

D

B

C

A

C

A

C

B

D

C

D

C

B

C

A

C

A

D

D

C

D

B

2

D

B

B

A

D

A

B

A

A

D

D

B

-

-

-

-

C

B

-

C

B

C

A

-

C

B

D

C

D

A

3

D

A

D

C

C

A

B

B

A

B

A

A

-

C

C

C

C

B

C

C

B

C

A

C

C

B

D

C

D

C

4

D

C

D

C

C

D

B

D

A

D

D

B

D

A

C

C

C

B

D

C

B

C

A

C

A

D

D

C

-

C

5

D

B

B

-

B

-

B

B

A

D

C

D

-

D

-

A

C

D

D

C

B

C

A

C

C

D

D

C

D

C

6

D

B

D

-

B

B

B

B

A

E

C

B

-

C

C

C

C

-

-

C

B

C

A

C

C

D

D

C

-

-

7

D

A

D

D

B

C

B

D

A

B

C

B

C

C

C

C

C

B

C

C

B

C

A

C

C

B

C

C

A

C

8

D

B

B

C

C

B

B

B

A

D

C

B

C

C

C

C

C

B

C

C

B

C

B

C

C

B

C

C

B

C

9

A

-

D

C

B

A

A

B

A

D

D

B

-

-

-

A

C

B

D

C

D

C

A

C

C

A

D

C

D

B

10

D

A

D

-

B

B

B

C

A

D

C

D

A

D

C

C

C

D

C

C

B

C

A

C

C

D

D

A

D

D

11

A

B

B

B

B

A

B

D

A

A

B

D

D

D

A

C

C

B

D

C

B

C

A

C

C

D

D

C

D

D

12

A

-

B

-

A

-

D

-

B

B

B

D

C

B

A

-

B

D

B

B

A

B

B

D

A

D

B

-

B

-

13

D

A

D

D

B

A

B

A

A

D

C

B

A

C

C

C

C

B

C

C

B

C

A

C

C

D

D

C

D

A

14

D

C

D

C

C

C

B

B

A

B

A

B

C

B

D

A

C

E

C

B

C

A

C

C

C

A

D

C

B

B

15

-

A

-

C

C

B

B

B

A

D

C

D

A

A

C

B

C

C

C

D

B

C

A

C

A

D

D

C

B

C

16

D

-

B

-

B

-

C

-

A

D

C

A

-

C

A

A

C

B

C

C

B

C

A

C

A

B

D

C

B

B

17

D

-

D

C

B

B

B

A

A

D

C

B

C

C

C

A

C

B

D

C

B

C

A

C

C

A

D

C

D

A

18

D

A

B

B

C

B

A

D

A

D

C

B

-

C

C

A

C

-

-

C

B

C

A

C

B

-

D

C

-

-

19

D

B

E

C

C

B

B

B

A

D

C

B

C

C

C

C

C

B

C

C

B

C

B

C

?

C

C

C

B

C

20

D

B

E

C

A

C

A

C

A

D

B

B

C

B

A

C

C

B

C

C

B

C

A

C

C

B

D

C

C

B

21

D

-

D

C

B

B

B

A

A

D

C

B

C

C

C

A

C

B

D

C

B

C

A

C

C

A

D

C

D

A

22

C

A

C

B

B

A

A

B

A

C

C

-

B

B

B

A

B

B

B

B

B

B

A

B

C

C

C

C

C

B

23

C

-

C

B

B

-

A

B

A

C

A

B

B

B

B

A

B

B

B

B

B

B

A

B

B

C

C

B

C

A

24

D

-

B

-

B

-

B

A

A

B

-

A

-

C

-

B

C

B

C

C

B

C

A

A

B

D

B

D

D

A

25

D

-

B

A

E

C

C

A

A

C

C

B

-

E

E

B

C

D

E

C

B

C

A

C

C

D

D

D

C

-

26

B

A

D

A

B

-

B

C

A

D

C

B

C

C

C

C

C

B

D

C

B

C

A

C

A

A

D

C

A

C

27

D

A

D

D

B

C

B

D

A

D

C

B

C

C

C

C

C

B

C

C

B

C

A

C

C

B

B

C

A

C

28

B

C

B

C

B

D

D

D

A

C

-

B

C

-

C

-

C

B

E

C

C

C

A

C

A

B

D

C

D

C

29

D

D

C

-

C

-

A

D

A

D

C

B

B

A

C

C

C

B

E

C

B

C

A

C

A

B

D

C

B

C

30

D

A

D

D

C

B

D

B

A

D

C

D

C

C

A

B

D

C

D

C

B

C

A

C

A

D

C

B

B

B

31

A

A

D

B

B

A

B

D

C

B

C

B

A

C

C

A

C

B

C

C

B

C

A

C

A

C

C

C

C

B

32

B

C

D

C

A

A

C

E

B

C

C

B

C

E

E

B

A

E

C

B

A

C

D

C

D

A

D

C

C

B

33

D

A

B

-

B

A

B

B

A

D

B

B

-

C

C

A

C

B

D

C

B

C

A

C

C

A

D

C

D

B

34

D

-

D

C

C

D

A

B

B

D

C

D

D

B

D

C

C

B

C

C

B

C

A

C

C

C

C

C

D

D

35

D

-

D

-

C

-

B

A

A

E

A

B

C

C

A

E

C

B

C

C

B

C

A

C

C

E

E

C

A

B

36

E

B

A

C

B

-

B

C

A

E

-

B

-

B

-

A

C

B

-

C

E

C

A

C

A

C

D

C

A

B

37

D

B

B

-

C

B

D

C

A

D

C

B

-

C

-

B

C

B

B

C

B

C

A

C

-

B

D

C

C

B

38

D

A

D

-

D

A

B

D

A

D

C

B

D

C

C

C

C

B

C

D

B

C

A

C

B

-

D

A

D

A

39

D

A

B

-

B

A

B

D

A

A

D

B

C

D

C

B

C

B

D

C

B

C

A

C

B

D

D

C

D

C

40

D

B

B

-

C

-

-

C

A

D

C

B

-

C

C

A

C

B

D

C

B

C

A

C

B

-

D

C

-

B

41

D

A

B

-

-

-

A

C

A

D

C

B

-

C

C

A

C

-

B

C

B

C

A

C

A

B

D

C

D

-

42

D

B

B

-

D

-

B

B

A

D

A

B

C

C

-

C

-

B

D

C

B

C

A

C

C

D

D

C

D

C

43

D

C

D

C

C

B

B

C

A

-

A

A

C

B

C

C

C

A

D

C

B

C

A

C

C

D

D

C

D

C

44

D

B

D

-

-

B

B

-

A

D

-

A

C

C

-

A

C

B

D

-

-

C

A

C

C

D

D

C

A

-

45

D

C

D

C

C

C

B

-

A

D

-

D

C

-

-

B

C

-

-

C

B

C

A

C

C

-

D

C

A

C

46

D

C

B

A

B

D

B

B

A

D

C

B

B

C

C

C

C

C

C

C

C

C

A

C

C

C

D

C

D

B

47

D

A

B

C

C

A

A

D

A

D

D

B

D

C

D

B

C

D

D

C

B

C

A

C

B

D

D

C

B

C

48

D

A

B

D

C

A

B

D

A

D

C

B

C

C

C

C

C

A

C

C

B

C

A

C

C

D

D

C

D

B

49

D

A

-

-

-

-

-

-

A

D

B

-

-

-

-

-

C

B

C

C

B

C

A

-

C

-

D

-

D

C

50

B

A

C

C

D

D

D

C

A

D

A

B

C

D

D

B

C

C

C

C

B

C

A

-

D

D

D

C

D

C

40

19

21

18

17

5

29

12

46

2

27

34

22

26

26

19

44

34

21

42

42

46

45

43

27

19

39

42

23

18

 [Source:  Data provided by AIU for its Correspondence Course participants for assignment purpose].
Find out the following statistical quantities
(1)  Mean,  (2)  Median,  (3)  Mode,  (4)  Standard Deviation,  (5)  Standard Error of Mean,  (6)  Reliability, and  (7)  Standard Error of  Measurement.

Sl.

No.

Marks

(x)

Frequency

(f)

xf

(x-x#)

(x - x#)²

(x-x#)² f

1

24

2

48

9

81

162

2

23

3

69

8

64

192

3

22

2

44

7

49

98

4

21

6

126

6

36

196

5

20

1

20

5

25

25

6

19

4

76

4

16

64

7

18

5

90

3

9

45

8

17

9

153

2

4

36

9

16

3

48

1

1

3

10

15

2

30

0

0

0

11

14

6

84

-1

1

6

12

13

2

26

-2

4

8

13

12

1

12

-3

9

9

14

10

1

10

-5

25

25

15

8

1

8

-7

49

49

16

5

1

5

-10

100

100

17

2

1

2

-13

169

169

åf  =  50

åxf  = 851

å  = 187