Is there a relationship between the number of sleeping

hours before the exam and the exam grade?

Introduction:

Many of

the students those days and especially exam days stress themselves on studying

and end up studying all night and getting minimal hours of sleep and very

little rest. Also, many of them think that it is the right to obtain maximal

results on the exam. Well many studies have shown that it is essential to get

enough hours of sleep in order to perform well on the exam and get an optimal

grade. “Dr. Philip

Alapat, medical director, Harris Health Sleep Disorders Center, and assistant

professor, Baylor College of Medicine, recommends students instead study

throughout the semester, set up study sessions in the evening (the optimal time

of alertness and concentration) and get at least 8 hours of sleep the night

before exams. “Memory recall and ability to maintain concentration are much

improved when an individual is rested,” he says. “By preparing early and being

able to better recall what you have studied, your ability to perform well on

exams is increased.”1

However, there has been people that I

personally know which does not fit in this fact as they get good grades while

studying all night long with minimal sleeping hours. This caused me to search

further to get extra evidence to know exactly how people are doing. To carry

out this task, 50 students , males and females in grade 11 and 12 will be asked

to note the numbers of hours they get before an exam and their grade.

Statement of task:

The main goal of this task is explore the

relationship between number of hours slept before an exam and their performance

on the exam which is determined by the grade. This will show whether there is a

positive, negative or no relationship between the two variables.

Plan of investigation:

The data should be collected and placed in a

table in which I plan to use those statistical methods which are Determining

the statistical basics of central tendencies by calculating the mean, mode,

median, lower quartile, upper quartile and interquartile as well as the

standard deviation from the collected results. Also, the graph of the line of

regression.The methods will also include the degree of freedom and correlation

co-efficient.

Those methods will be done to show whether

there is a relationship between hours of sleep and the exam grade.

Data collection:

The number of hours slept

The grade on exam (%)

The number of hours slept

The grade on exam (%)

5

87

6

94

1

66

2

67

9

89

3

75

7

94

4

66

3

77

1

70

9

93

1

75

0

77

1

67

3

69

0

69

2

73

8

86

11

89

9

93

8

96

10

92

7

90

12

75

8

94

12

91

6

93

8

90

6

89

2

66

0

76

4

66

3

68

0

76

5

66

9

98

6

72

6

94

7

88

3

76

9

95

3

70

7

80

9

87

2

66

4

66

2

69

7

87

1

67

3

73

Mathematical processing:

Table for midpoint :

Number of hours slept

Frequency

Total Frequency

(f1)

Midpoint (x1)

(f1) * (x1)

0?x<2
9
1
9
2?x<4
12
3
36
4?x<6
5
5
25
6?x<8
10
7
70
8?x<10
10
9
90
10?x<13
4
11.5
46
Total
50
276
Pie chart:
Cumulative frequency table of the hours of sleep:
Hours (hr)
Frequency (f)
Cumulative frequency
1
9
9
3
12
21
5
5
26
7
10
36
9
10
46
11.5
4
50
Cumulative frequency graph:
Mean: It is the sum of all the values divided by the
number of values. In this case the mean is estimated.
Mean: 276/50= 5.52
Mode: it is the most common value in the set of data
and in the table it is the interval with the greatest frequency.
The mode is 2?x<4.
Median: it is the value that lies in the middle when
the data are arranged in size order.
Median: (50+1)/2 = 25.5 so the median 5
Lower quartile: it is
the median of the lower half of the data.
Lower quartile: (50+1)/4 = 12.75 so the lower
quartile 3
Upper quartile: it is
the median of the upper half of the data.
Upper quartile: 3*(50+1) /4 = 38.25 so the
upper quartile is 9
The interquartile range: it is
the difference between the lower and upper quartile.
IQR=
9-3=6
Grade on the exam
Frequency
Total Frequency
(f1)
Midpoint (x1)
(f1) * (x1)
65