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ANALYSE AND INTERPRETATION OF TEST SCORES

Pie Chart

Score ( x ) Frequency ( f )
25 1
24 1
21 3
20 3
19 3
18 2
17 3
16 3
15 3
14 2
13 2
11 1
10 1
9 2
Total 30

Pie Chart of 3 Dinamik Scores
25 24
10
11 3% 3%
13 3%
3%
7% 9
21
7%
10%
20
14
10%
7%
15 19
10% 10%
16 18
10% 17 7%
10%

The pie chart shows that:

1. 3% represents only 1 candidate who obtains 25 marks, 24 marks, 11 marks and 10 marks.
2. 7% represents 2 candidates who obtain 18 marks, 14 marks, 13 marks, and 9 marks.
3. 10% represents 3 candidates who obtain 21 marks, 20 marks, 19 marks, 17 marks, 16 marks and
15 marks.

Histogram

Class Interval Class Boundary Frequency

9 – 11 8.5 – 11.5 4

12 – 14 11.5 – 14.5 4

15 – 17 14.5 – 17.5 9

18 – 20 17.5 – 20.5 8

21 – 23 20.5 – 23.5 3

24– 26 23.5 – 26.5 2

Total 30

Histogram of 3 Dinamik Scores
10
9
8
7
Frequency

6
5
4
3
2
1
0
8.5 – 11.5 11.5 – 14.5 14.5 – 17.5 17.5 – 20.5 20.5 – 23.5 23.5 – 26.5
Scores

From the histogram, we can conclude that:

1. The score which most candidates obtained is 14.5-17.5.
2. The number of candidates who obtained the most scores within 14.5-17.5 is 9.
3. The total number of candidates who obtained sores within 17.5-20.5 is 8.
4. On the whole, the performance of the candidates is satisfactory because half of the candidates
obtained high marks.

Frequency Polygon

Class Interval Class Boundary Class Mark Frequency

9 – 11 8.5 – 11.5 10 4

12 – 14 11.5 – 14.5 13 4

15 – 17 14.5 – 17.5 16 9

18 – 20 17.5 – 20.5 19 8

21 – 23 20.5 – 23.5 22 3

24– 26 23.5 – 26.5 25 2

Total 30

Frequency Polygon of 3 Dinamik Scores
10
9
8
7
Frequency

6
5
4
3
2
1
0
0 8.5 – 11.5 11.5 – 14.5 14.5 – 17.5 17.5 – 20.5 20.5 – 23.5 23.5 – 26.5
Scores

Frequency Curve of 3 Dinamik Scores
10
9
8
7
Frequency

6
5
4
3
2
1
0
0 1 2 3 4 5 6 7
Scores

Ogive

Cumulative
Class Interval Upper Class Boundary Frequency
Frequency

9 – 11 11.5 4 4

12 – 14 14.5 4 8

15 – 17 17.5 9 17

18 – 20 20.5 8 25

21 – 23 23.5 3 28

24– 26 26.5 2 30

Ogive of 3 Dinamik Scores
35

30

25
Frequency

20

15

10

5

0
15
8.5 – 11.5 11.5 – 14.5 14.5 – 17.5 17.5 – 20.5 20.5 – 23.5 23.5 – 26.5
Scores

Percentage Ogive

Percentage
Upper Class Cumulative
Class Interval Frequency Cumulative
Boundary Frequency
Frequency

9 – 11 11.5 4 4 13.3

12 – 14 14.5 4 8 26.7

15 – 17 17.5 9 17 56.7

18 – 20 20.5 8 25 83.3

21 – 23 23.5 3 28 93.3

24– 26 26.5 2 30 100

Total 30

Percentage Ogive of 3 Dinamik Scores
35

30 100%

25
75%
Frequency

20

15 50%

10
25%
5

0
8.5 – 11.5 11.5 – 14.5 14.5 – 17.5 17.5 – 20.5 20.5 – 23.5 23.5 – 26.5
Scores

From the ogive, we can find that:

1. The number of candidates who failed, if the passing mark is 15 marks are 8 candidates.
2. The number of candidates who would obtain grade A, if grade A is 25 marks and above is only
one candidate.

Scatter plots

Score ( x ) Frequency ( f )
25 1
24 1
21 3
20 3
19 3
18 2
17 3
16 3
15 3
14 2
13 2
11 1
10 1
9 2
Total 30

Scatter Plots of 3 Dinamik Scores
3.5

3

2.5
Frequency

2

1.5

1

0.5

0
0 5 10 15 20 25 30
Scores

From the scatter plots, we can find that:

1. There are 3 groups of pupils: high, moderate and low performers.

MEASURES OF CENTRAL TENDENCY

Mean, Median and Mod

Class Interval ( x ) Class Mark ( x ) Frequency ( f ) (f)(x)

9 – 11 10 4 40

12 – 14 13 4 52

15 – 17 16 9 144

18 – 20 19 8 152

21 – 23 22 3 66

24– 26 25 2 50

Mean,

Median,

Where L = lower class boundary of median class

N= number of items in data

s= cumulative frequency of all classes prior to the median class

= frequency of median class

C= size of median class interval

Class Boundary Frequency Cumulative Frequency

8.5 – 11.5 4 4

11.5 – 14.5 4 8

14.5 – 17.5 9 17

17.5 – 20.5 8 25

20.5 – 23.5 3 28

23.5 – 26.5 2 30

Mode,

Where L = lower class boundary of modal class

= frequency of modal class – frequency before modal class

= frequency of modal class – frequency after modal class

C= class width

Class Boundary Frequency

8.5 – 11.5 4

11.5 – 14.5 4

14.5 – 17.5 9

17.5 – 20.5 8

20.5 – 23.5 3

23.5 – 26.5 2

Mode obtained from histogram :

Histogram of 3 Dinamik Scores
10
9
8 Mode
7
Frequency

6
5
4
3
2
1
0
17
8.5 – 11.5 11.5 – 14.5 14.5 – 17.5 17.5 – 20.5 20.5 – 23.5 23.5 – 26.5
Scores

MEASURES OF VARIABILITY

Range, Variance and Standard Deviation

Range = Highest Score – Lowest Score

= 25 – 9

= 16

Differences Squared,
Score ( x ) Differences,

25 25 – 16.8 = 8.2 67.24
24 24 – 16.8 = 7.2 51.84
21 21 – 16.8 = 4.2 17.64
20 20 – 16.8 = 3.2 10.24
19 19 – 16.8 = 2.2 4.84
18 18 – 16.8 = 1.2 1.44
17 17 – 16.8 = 0.2 0.04
16 16 – 16.8 = -0.8 0.64
15 15 – 16.8 = -1.8 3.24
14 14 – 16.8 = -2.8 7.84
13 13 – 16.8 = -3.8 14.44
11 11 – 16.8 = -5.8 33.64
10 10 – 16.8 = -6.8 46.24
9 9 – 16.8 = -7.8 60.84
Total = 232 Total = 320.16

Variance

=

=

=

Standard Deviation

=

=

=

=

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