statistics

Topics: Median, Standard deviation, Skewness Pages: 13 (1130 words) Published: September 28, 2014
TITLE:
To determine whether standard 3 students of San Fernando Boys’ Government School perform better in Mathematics than Mental Mathematics

STATEMENT OF TASK
Mathematics is a very important subject taught in all schools. Mental mathematics compliments the regular mathematics and therefore both are tested in primary schools. Mathematics is the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.

The Standard 3 class is where the transition from junior to senior level occurs where teachers expect the transference of concrete to abstract thinking would have occurred.

A common theory by many primary school teachers is ‘Students perform better in Mathematics than Mental math. Mental math is something that has to be developed and involves critical thinking. Mental math requires quick thinking and the student must solve the problem in their minds whereas in regular mathematics, the problem can be solved visually. Therefore, teachers should take these factors into consideration while testing and marking students in these areas.’

In this study, the statistics of 30 students of a standard 3 class of San Fernando Boys’ Government School will be analysed to determine the truth of this theory.

DATA COLLECTION METHODS

Mathematics and mental mathematics marks of term 1 of the class of 2013 were obtained from a Standard 3 teacher of San Fernando Boys’ Government School. The marks were divided into the form:
Mathematics Marks, x
Mental Mathematics marks, y

DATA PRESENTATION AND ANALYSIS

Sample number
Marks earned (x)

1
70
4900
2
86
7396
3
49
2401
4
66
4356
5
94
8836
6
68
4624
7
92
8464
8
96
9216
9
76
5776
10
71
5041
11
83
6889
12
59
3481
13
65
4225
14
98
9604
15
80
6400
16
68
4624
17
72
5184
18
85
7225
19
100
10000
20
69
4761
21
61
3721
22
80
6400
23
87
7569
24
95
9025
25
63
3969
=1933
=154087

Table 1: Sample data of marks earned by students in Mathematics examinations

Sample Number
Marks Earned (y)

1
40
1600
2
93
8649
3
26
676
4
53
2809
5
100
10000
6
46
2116
7
93
8649
8
86
7396
9
39
1521
10
46
2116
11
74
5476
12
60
3600
13
40
1600
14
86
7396
15
66
4356
16
45
2025
17
61
3721
18
87
7569
19
48
2304
20
55
3025
21
75
5625
22
62
3844
23
24
576
24
60
3600
25
33
1089
=1498
=101338

Table 2 of marks earned by students in Mental Mathematics

Calculation of Measures of Spread (mean, variance and standard deviation) of mathematics and mental mathematics marks.

Mean =
=
=77.32
Variance S² =
=
=185.098

Standard Deviation S =
=
=13.61

Mean =
=
= 59.92

Variance S² =
=
=463.11

Standard S =
Deviation =
=21.52

STEM AND LEAF DIAGRAM
Mathematics

Mental Mathematics

9
9
9 8 8 6 5 3 1
6 2 1 0
7 6 5 3 0 0
8 6 5 4 2
0
0
1
2
3
4
5
6
7
8
9
10

4 6
3 9
0 0 5 6 6 8
3 5
0 0 1 2 6
4 5
6 6 7
3 3
0
Key: 9 4 represents 49 marks

Key: 5 3 represents 53 marks
Figure 1: Stem and leaf diagram of marks earned in Mathematics and Mental Mathematics

Calculation of the median Q1, Q3, inter-quartile range, maximum and minimum values of mathematics and mental mathematics

Mathematics
Mental...
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