Test Analysis And Measure Of Central Tendency
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Test Scores Key Student #
#Total #Correct #Incorrect p
C Q1 11 C 16 C 2C 3C 25 C 14 C 13 C 20 C 5C 4C 12 C 8C 9C 18 C 23 C 10 C 6C 21 C 7B 22 B 17 B 15 C 1C 24 C 19 D
B Q2 B B B B B B B B B B B B B B B B A A B B B B B B C
D Q3 D D D D D D D D D D D D D B D B D D A A C D B B A
D Q4 D D D D D A A D C B D B A D B A D D B B C D A A D
B Q5 B B B B B B B B B B B B B B B B C C B B B B C C B
C Q6 C C D C D C C C C C C C C A C C C C C C A B D D A
D Q7 D D A D A D D D B B D B D D B D A A B B D A A A B
A Q8 A A A A A A A A A A D D D D D C D D B B D A
A
C Q9 C C C C C C C C C C D B B D B D C C D D C B D D D
B Q10 B B B B B B B A D B A C D D C C D D D D D D D C
A Q11 A A A A A A A C A A A A A A A A A A A A A A A A C
C Q12 C C C C C C C D C C C C C C C B C C C C D C D D D
B Q13 B B B B B B B B B A A B B A B A A A B B B D A A A
D Q14 D D D D D D D D D D D D D D D D D D D D D A A A A
A Q15 A A A A A A A A A C A A A A A D A A C C A A A A D
A Q16 A A A A A A A A A A A A A A A A A A A A
C Q17 C C C C C A A C A C C C C C C C A A A A
C A A B
B C C B
25 25 25 25 25 25 25 23 25 24 25 25 25 25 25 24 24 21 22 17 12 21 17 11 12 13 8 23 19 15 21 20 22 15 4 3 8 13 4 8 14 11 12 16 2 6 10 4 5 2 9 84.00 88.00 68.00 48.00 84.00 68.00 44.00 52.17 52.00 33.33 92.00 76.00 60.00 84.00 80.00 91.67 62.50
#Correctupper level #Correctlower level D (Discrimination index)
15.00 15.00 14.00
8.00 15.00 12.00
9.00 10.00 10.00
8.00 14.00 14.00 12.00 15.00 14.00 15.00 12.00
6.00
7.00
3.00
4.00
6.00
5.00
2.00
2.00
3.00
0.00
9.00
5.00
3.00
6.00
6.00
7.00
3.00
0.60
0.53
0.73
0.27
0.60
0.47
0.47
0.53
0.47
0.53
0.33
0.60
0.60
0.60
0.53
0.53
0.60
Quantitative Item Analysis D Q18 D D D B D B D B B B A B B A D B B D D C B B B B
B Q19 B B B D B B B B B C B B D B B B D D D D A D D D A
C Q20 C C C C C C C C C C D A A C A C C C C C D D B B B
24 25 25 8 13 16 16 12 9 33.33 52.00 64.00
Q1
Q2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0
Discrimination index (D) Difficulty Index (p) q pq
Q3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0
Q4
Q5
1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0
1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1
0.6 0.53 0.73
0.27
0.84 0.88 0.68 0.16 0.12 0.32 0.13 0.11 0.22
Q6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1
Q7 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0
Q8 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0
Q9 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0
Q10 Q11 Q12 Q13 Q14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
0.6 0.47 0.47 0.53 0.47 0.53 0.33
0.6
0.6
0.6
0.48 0.84 0.68 0.44 0.52 0.52 0.33 0.92 0.76 0.60 0.84 0.52 0.16 0.32 0.56 0.48 0.48 0.67 0.08 0.24 0.40 0.16 0.25 0.13 0.22 0.25 0.25 0.25 0.22 0.07 0.18 0.24 0.13
5.00 12.00 11.00
Total of pq-values
3.830
3.00
1.00
5.00
Variance
499.553
0.13
0.73
0.40
Standard deviation (SD)
21.83
KR21
0.33
1 2 3
1.05 2990 9530.4
Mean
66
Median
65
Mode
65
Range (R)
85
em Analysis Q15 Q16 Q17 Q18 Q19 Q20 Total 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0.53 0.53
0.6 0.13 0.73
0.4
0.80 0.92 0.63 0.33 0.52 0.64 0.20 0.08 0.38 0.67 0.48 0.36 0.16 0.08 0.23 0.22 0.25 0.23
% Level 20 100.00 u 20 100.00 u 18 90.00 u 18 90.00 u 18 90.00 u 17 89.47 u 17 85.00 u 17 85.00 u 15 75.00 u 14 70.00 u 14 70.00 u 13 65.00 u 13 65.00 u 13 65.00 u 13 65.00 u 12 60.00 l 11 55.00 l 11 55.00 l 10 50.00 l 10 50.00 l 8 47.06 l 9 45.00 l 6 31.58 l 6 31.58 l 3 15.00 l
Simple Frequency Distribution Score Frequency (f) 100 2 90 3 89 1 85 2 75 1 70 2 65 4 60 1 55 2 50 2 47 1 45 1 32 2 15 1
Grouped Frequency Distribution Frequency Histogram 6 5 Frequency (f)
Lower limit (LL) Upper limit (UL) Intervals Frequency (f) Midpoint (MP) 9 17 9-17 1 13 18 26 18-26 0 22 27 35 27-35 2 31 36 44 36-44 0 40 45 53 45-53 4 49 54 62 54-62 3 58 63 71 63-71 6 67 72 80 72-80 1 76 81 89 81-89 3 85 90 98 90-98 3 94 99 107 99-107 2 103
4 3 2 1 0 9-17
Range (R)
85
Interval width (i) Rounded i-value
8.5 9
18-26
27-35
36-44
45-53
54-62
63-71
7
Intervals (i)
Frequency Polygon 6 5
Mean Median Mode
66 65 65
Frequency (f)
Student # Score 11 100 16 100 2 90 3 90 25 90 14 89 13 85 20 85 5 75 4 70 12 70 8 65 9 65 18 65 23 65 10 60 6 55 21 55 7 50 22 50 17 47 15 45 1 32 24 32 19 15
4 3 2 1 0 Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10 R
Midpoint (MP)
Fre
2 1 0 Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10 R
Midpoint (MP)
Frequency Histogram
4
45-53
54-62
63-71
72-80
81-89
90-98
99-107
Intervals (i)
Frequency Polygon
7
Row 8
Row 9
Row 10 Row 11 Row 12 Row 13 Row 14
Midpoint (MP)
7
Row 8
Row 9
Row 10 Row 11 Row 12 Row 13 Row 14
Midpoint (MP)
Measures of Tendency and Variability Score
x 100 100 90 90 90 89 85 85 75 70 70 65 65 65 65 60 55 55 50 50 47 45 32 32 15
x2 34 34 24 24 24 23 19 19 9 4 4 -1 -1 -1 -1 -6 -11 -11 -16 -16 -19 -21 -34 -34 -51
1156 1156 576 576 576 529 361 361 81 16 16 1 1 1 1 36 121 121 256 256 361 441 1156 1156 2601
The Normal Distribution
Mean Median Mode
66 65 65
∑x2
11913
Range (R)
85
Standard deviation (SD)
21.83
#Total #Correct #Incorrect p
C Q1 11 C 16 C 2C 3C 25 C 14 C 13 C 20 C 5C 4C 12 C 8C 9C 18 C 23 C 10 C 6C 21 C 7B 22 B 17 B 15 C 1C 24 C 19 D
B Q2 B B B B B B B B B B B B B B B B A A B B B B B B C
D Q3 D D D D D D D D D D D D D B D B D D A A C D B B A
D Q4 D D D D D A A D C B D B A D B A D D B B C D A A D
B Q5 B B B B B B B B B B B B B B B B C C B B B B C C B
C Q6 C C D C D C C C C C C C C A C C C C C C A B D D A
D Q7 D D A D A D D D B B D B D D B D A A B B D A A A B
A Q8 A A A A A A A A A A D D D D D C D D B B D A
A
C Q9 C C C C C C C C C C D B B D B D C C D D C B D D D
B Q10 B B B B B B B A D B A C D D C C D D D D D D D C
A Q11 A A A A A A A C A A A A A A A A A A A A A A A A C
C Q12 C C C C C C C D C C C C C C C B C C C C D C D D D
B Q13 B B B B B B B B B A A B B A B A A A B B B D A A A
D Q14 D D D D D D D D D D D D D D D D D D D D D A A A A
A Q15 A A A A A A A A A C A A A A A D A A C C A A A A D
A Q16 A A A A A A A A A A A A A A A A A A A A
C Q17 C C C C C A A C A C C C C C C C A A A A
C A A B
B C C B
25 25 25 25 25 25 25 23 25 24 25 25 25 25 25 24 24 21 22 17 12 21 17 11 12 13 8 23 19 15 21 20 22 15 4 3 8 13 4 8 14 11 12 16 2 6 10 4 5 2 9 84.00 88.00 68.00 48.00 84.00 68.00 44.00 52.17 52.00 33.33 92.00 76.00 60.00 84.00 80.00 91.67 62.50
#Correctupper level #Correctlower level D (Discrimination index)
15.00 15.00 14.00
8.00 15.00 12.00
9.00 10.00 10.00
8.00 14.00 14.00 12.00 15.00 14.00 15.00 12.00
6.00
7.00
3.00
4.00
6.00
5.00
2.00
2.00
3.00
0.00
9.00
5.00
3.00
6.00
6.00
7.00
3.00
0.60
0.53
0.73
0.27
0.60
0.47
0.47
0.53
0.47
0.53
0.33
0.60
0.60
0.60
0.53
0.53
0.60
Quantitative Item Analysis D Q18 D D D B D B D B B B A B B A D B B D D C B B B B
B Q19 B B B D B B B B B C B B D B B B D D D D A D D D A
C Q20 C C C C C C C C C C D A A C A C C C C C D D B B B
24 25 25 8 13 16 16 12 9 33.33 52.00 64.00
Q1
Q2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0
Discrimination index (D) Difficulty Index (p) q pq
Q3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0
Q4
Q5
1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0
1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1
0.6 0.53 0.73
0.27
0.84 0.88 0.68 0.16 0.12 0.32 0.13 0.11 0.22
Q6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1
Q7 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0
Q8 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0
Q9 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0
Q10 Q11 Q12 Q13 Q14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
0.6 0.47 0.47 0.53 0.47 0.53 0.33
0.6
0.6
0.6
0.48 0.84 0.68 0.44 0.52 0.52 0.33 0.92 0.76 0.60 0.84 0.52 0.16 0.32 0.56 0.48 0.48 0.67 0.08 0.24 0.40 0.16 0.25 0.13 0.22 0.25 0.25 0.25 0.22 0.07 0.18 0.24 0.13
5.00 12.00 11.00
Total of pq-values
3.830
3.00
1.00
5.00
Variance
499.553
0.13
0.73
0.40
Standard deviation (SD)
21.83
KR21
0.33
1 2 3
1.05 2990 9530.4
Mean
66
Median
65
Mode
65
Range (R)
85
em Analysis Q15 Q16 Q17 Q18 Q19 Q20 Total 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0.53 0.53
0.6 0.13 0.73
0.4
0.80 0.92 0.63 0.33 0.52 0.64 0.20 0.08 0.38 0.67 0.48 0.36 0.16 0.08 0.23 0.22 0.25 0.23
% Level 20 100.00 u 20 100.00 u 18 90.00 u 18 90.00 u 18 90.00 u 17 89.47 u 17 85.00 u 17 85.00 u 15 75.00 u 14 70.00 u 14 70.00 u 13 65.00 u 13 65.00 u 13 65.00 u 13 65.00 u 12 60.00 l 11 55.00 l 11 55.00 l 10 50.00 l 10 50.00 l 8 47.06 l 9 45.00 l 6 31.58 l 6 31.58 l 3 15.00 l
Simple Frequency Distribution Score Frequency (f) 100 2 90 3 89 1 85 2 75 1 70 2 65 4 60 1 55 2 50 2 47 1 45 1 32 2 15 1
Grouped Frequency Distribution Frequency Histogram 6 5 Frequency (f)
Lower limit (LL) Upper limit (UL) Intervals Frequency (f) Midpoint (MP) 9 17 9-17 1 13 18 26 18-26 0 22 27 35 27-35 2 31 36 44 36-44 0 40 45 53 45-53 4 49 54 62 54-62 3 58 63 71 63-71 6 67 72 80 72-80 1 76 81 89 81-89 3 85 90 98 90-98 3 94 99 107 99-107 2 103
4 3 2 1 0 9-17
Range (R)
85
Interval width (i) Rounded i-value
8.5 9
18-26
27-35
36-44
45-53
54-62
63-71
7
Intervals (i)
Frequency Polygon 6 5
Mean Median Mode
66 65 65
Frequency (f)
Student # Score 11 100 16 100 2 90 3 90 25 90 14 89 13 85 20 85 5 75 4 70 12 70 8 65 9 65 18 65 23 65 10 60 6 55 21 55 7 50 22 50 17 47 15 45 1 32 24 32 19 15
4 3 2 1 0 Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10 R
Midpoint (MP)
Fre
2 1 0 Row 4
Row 5
Row 6
Row 7
Row 8
Row 9
Row 10 R
Midpoint (MP)
Frequency Histogram
4
45-53
54-62
63-71
72-80
81-89
90-98
99-107
Intervals (i)
Frequency Polygon
7
Row 8
Row 9
Row 10 Row 11 Row 12 Row 13 Row 14
Midpoint (MP)
7
Row 8
Row 9
Row 10 Row 11 Row 12 Row 13 Row 14
Midpoint (MP)
Measures of Tendency and Variability Score
x 100 100 90 90 90 89 85 85 75 70 70 65 65 65 65 60 55 55 50 50 47 45 32 32 15
x2 34 34 24 24 24 23 19 19 9 4 4 -1 -1 -1 -1 -6 -11 -11 -16 -16 -19 -21 -34 -34 -51
1156 1156 576 576 576 529 361 361 81 16 16 1 1 1 1 36 121 121 256 256 361 441 1156 1156 2601
The Normal Distribution
Mean Median Mode
66 65 65
∑x2
11913
Range (R)
85
Standard deviation (SD)
21.83
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