Does Age Effect Grade Point
Average?
By Amanda Darrow and
Dennis de Melo
Does age determine a higher or lower
grade point average? By Using a
sample of 50 from the population of
Salt Lake Community College
Students, we will determine if there
is in fact a correlation between age
and G.P.A.
Collecting the Data
A questionnaire was handed out to 50 Salt Lake
Community College Students.
The questionnaire asked two questions:
• The participants age
• The participants grade point average
Charts: Averages and Samples
Age
18
Average
G.P.A
2.6
19
2.5
20
2.9
21
2.8
22
2.7
23
3.1
24
3.1
25
3.9
26
2.7
28
3.3
29
3.4
30
2.8
31
3.3
33
3.7
35
2.6
36
3.7
38
3.2
39
4.0
42
3.9
Age
(18-42)
Number of
Samples
18-19
12
20-21
8
22-23
5
24-25
4
26-27
5
28-29
4
30-31
4
32-33
2
34-35
1
36-37
2
38-39
2
42
1
Grade Point Average
Number of Samples
1.9
1
2.0
1
2.2
2
2.3
1
2.4
2
2.5
2
2.6
6
2.7
3
2.8
4
3.0
1
3.1
1
3.2
5
3.3
4
3.6
4
3.7
3
3.8
3
3.9
2
4.0
2
Age Statistics
•
•
•
•
Mean: 23.5
Range: 42-18= 24
Mode= 19
Outliers: No Outliers
Age 5-Number Summary
•
•
•
•
•
L=18
Q1= 20
µ= 23.5
Q3= 29
H= 42
IQR: 29-20= 9
Lower Fence:0-1.5(9) = 6.5
Upper Fence: 29 + 1.5(9) = 42.5
Age Standard Deviation
18-19 = 12
12-4.2=7.8
7.8²= 60.84
20-21 = 8
8-4.2= 3.8
3.8²= 14.44
22-23 = 5
5-4.2= 0.8
0.8²= 0.64
24-25 = 4
4-4.2= -0.2 -0.2²= 0.04
25-27 = 5
5-4.2= 0.8
28-29 = 4
4-4.2= -0.2 -0.2²= 0.04
30-31 = 4
4-4.2= -0.2 -0.2²= 0.04
32-33 = 2
2-4.2= -2.2 -2.2²= 4.84
34-35 = 1
1-4.2= -3.2 -3.2²= 10.24
36-37 = 2
2-4.2= -2.2 -2.2²= 4.84
38-39 = 2
2-4.2= -2.2 -2.2²= 4.84
42
1-4.2= -3.2 -3.2²= 10.24
=1
0.8²= 0.64
∑(x) = 50
µx= 50/12= 4.2
∑(X1-µ) = 111.68
111.68/12= 9.31
√9.31 = 3.05
G.P.A. Statistics
Mean: 3.1
• Range: 4.0-2.5 = 1.5
• Mode= 2.6, 2.7, 2.8, 3.1, 3.3, 3.7
and 3.9
• Outliers: No Outliers
•
G.P.A. 5-Number Summary
•
•
•
•
•
L=2.5
Q1= 2.75
µ= 3.1
Q3= 3.55
H= 4.0
IQR: 3.55-2.75= 0.8
LF: 2.75- 1.5(0.8) = 1.55
UF: 3.55 + 1.5(0.8) = 4.75
G.P.A Standard Deviation
18-19 = 2.6
2.6-3.3=-0.7 -0.7²= 0.49
20-21 = 2.9
2.9-3.3=-0.4 -0.4²= 0.16
22-23 = 2.9
2.9-3.3=-0.4 -0.4²= 0.16
24-25 = 3.5
3.5-3.3=0.2
26-27 =2.7
2.7-3.3=-0.6 - 0.6²= 0.36
28-29 = 3.4
3.4-3.3=0.1
30-31 = 3.1
3.1-3.3=-0.2 -0.2²= 0.04
32-33 = 3.7
3.7-3.3=0.4
0.4²= 0.16
34-35 = 3.6
3.6-3.3=0.3
0.3²= 0.09
36-37 = 3.7
3.7-3.3=0.4
0.4²= 0.16
38-39 = 3.6
3.6-3.3=0.3
0.3²= 0.09
42
3.9-3.3=0.6
0.6²= 0.36
= 3.9
0.2²= 0.04
0.1²= 0.01
∑(x) = 39.6
∑(X1-µ) = 2.12
µx=9.6/12=3.3
2.12/12= 0.177
√0.177= 0.421
Linear Correlation Coefficient
Age
18
Average
G.P.A
2.6
19
2.5
20
2.9
21
2.8
22
2.7
23
3.1
24
3.1
25
3.9
26
2.7
28
3.3
29
3.4
30
2.8
31
3.3
33
3.7
35
2.6
36
3.7
38
3.2
39
4.0
42
3.9
Correlation:
0.643159696
N=19-1 = 18
Table II:
18 = 0.468
Since the final
coefficient is smaller
than the correlation we
have a linear relation