scores of students
TRANSCRIPT
INTRODUCTION
Statistic is a process which involves the steps of collecting, arranging, making
analysis and interpreting data. It is a discipline which is concerned with designing
experiments and other data collection, summarizing information to aid understanding,
drawing conclusions from data, and estimating the present or predicting the future.
Statistics plays a vital role in every fields of human activity. Statistics has
important role in determining the existing position of per capita income, unemployment,
population growth rate, housing, schooling medical facilities and others. In the contexts
of school system, the most important thing is the collection of marks of the various
subjects.
In statistic, the measures that used are mode, mean, median, standard deviation
and others. The mode is the value that occurs the most frequently in a data set or
a probability distribution. The mean is the sum of all the scores divided by the number
of scores. The median is the middle of a distribution, half the scores are above the
median and half are below the median. Variance is the average squared deviation of
each number from its mean while standard deviation is equal to the square root of the
arithmetic mean of the squares of the deviations from the arithmetic mean.
Scores of students
Frequency(f)
Midpoint(x)
fx fx2 Cumulative Frequency
0-10 0 5.5 0 0 0
11-20 0 15.5 0 0 0
21-30 2 25.5 51 300.5 2
31-40 5 35.5 177.5 6301.25 7
41-50 4 45.5 182 8281 11
51-60 9 55.5 499.5 27722.25 20
61-70 8 65.5 524 34322 28
71-80 1 75.5 75.5 5700.25 29
81-90 1 85.5 85.5 7310.25 30
91-100 0 95.5 0 0 30
5 DELIMA
From the data :
Mode : 51-60
Mean : x= ∑fx∑ f
= 51+177.5+182+499.5+524+75.5+85.5
32
= 1595
30
= 53.17
Median : T 1+n
2 = the 1+n2 th term
30+1 = 15.5
2
Hence, 50.5 + ( 30/2 -11 ) 10
9
= 54.94
Standard deviation : : σ = √∑ f x2∑ f−(x) ²
√ 300.5+6310.25+8281+27722.25+34322+5700.25+7310.2530 -
2827.05
√ 89946.530 - 2827.05
= √2998.22−2827.05
= √171.17
= 13.08
5 FAIRUZ
From the data:
Scores of students
Frequency(f)
Midpoint(x)
fx fx2 Cumulative Frequency
0-10 2 5.5 11 60.5 2
11-20 12 15.5 186 2883 14
21-30 7 25.5 178.5 4551.75 21
Mode : 11-20
Mean : x= ∑fx∑ f
= 11+186+178.5
21
= 375.5
21
= 17.88
Median : T 1+n
2 = the 1+n2 th term
21+1 = 11
2
Hence, 10.5 + ( 21/2 -2 ) 10
12
= 17.58
Standard deviation : : σ = √∑ f x2∑ f−(x) ²
√ 60.5+2883+4551.7521 – 319.69
=√ 7495.2521 - 319.69
= √356.92 - 319.69
= √37.23
= 6.10
Number of students of year 5D that score in Mathematic Examination
1-10 marks
11-20 marks
21-30 marks
31-40 marks
41-50 marks
51-60 marks
61-70 marks
71-80 marks
81-90 marks
0
1
2
3
4
5
6
7
8
9
10
Number of students
Number of students
1-10 marks
11-20 marks
21-30 marks
31-40 marks
41-50 marks
51-60 marks
61-70 marks
71-80 marks
81-90 marks
0
1
2
3
4
5
6
7
8
9
10
Number of students
Number of students
2
2
5
4
9
8
1 1
Number of students
1-10 marks11-20 marks21-30 marks31-40 marks41-50 marks51-60 marks61-70 marks71-80 marks81-90 marks
22
5
49
8
1 1
Number of students
1-10 marks11-20 marks21-30 marks31-40 marks41-50 marks51-60 marks61-70 marks71-80 marks81-90 marks
Number of students of year 5F that score in Mathematic Examination
1-5marks 6-10marks 11-15marks 16-20marks 21-25marks 26-30marks0
1
2
3
4
5
6
7
8
Numbers of students
Numbers of students
1-5marks 6-10marks 11-15marks 16-20marks 21-25marks 26-30marks0
1
2
3
4
5
6
7
8
Numbers of students
Numbers of students
2
6
7
5
1
Numbers of students
1-5marks6-10marks11-15marks16-20marks21-25marks26-30marks
1-5marks 6-10marks 11-15marks
16-20marks
21-25marks
26-30marks
0
1
2
3
4
5
6
7
Numbers of students
Numbers of students
2
6
7
5 1
Numbers of students
1-5marks6-10marks11-15marks16-20marks21-25marks26-30marks
After collecting and analyzing the data, we can make some comparisons between the
two classes. 5 Delima is the first class while 5 Fairuz the last class, so we can see a big
differences of the achievement scores.
For class 5 Delima, the mode is 51-60, while the mode for class 5 Fairuz is 11-20. As a
first class, most of the students in 5 Delima got average marks but in class 5 Fairuz,
most of them got low marks. The mean of class 5 Delima is higher than class 5 Fairuz
which is 53.17. This is because the sum of value of data of 5 Delima students is higher.
As the sum of data of 5 Fairuz students is low, hence the mean is also smaller which is
17.88.
The median of class 5 Delima is 54.94 while for the other class is 17.58. We can see
that the differences of the scores also give effects to median just like the mean. For
standard deviation, 5 Delima also got the higher value which is 13.08 compared to 5
Fairuz which just got 6.10. The reasons is the marks that students in 5 Delima got has a
difference to each other while the marks of students in 5 Fairuz is almost the same.
From the result, we can assume some factors that affect the result of statistics. Firstly,
the students in 5 Delima are the excellent students whereas the students in 5 Fairuz are
the average students. Maybe the 5 Fairuz’s students are also did not focus in the class.
That is why their marks are low. They are also did not interested to study compared to 5
Delima students.
