Research Methods: CGPA, Descriptive Statistics, Correlation Coefficient, Linear Regression

RESEARCH METHODS
STUDENT ID:
[Pick the date]

Question 1
Mean and standard deviation of CGPA
Mean = Sum of data points/ number of data points
x= 1
n ∑ x
∑ x =265.160
n=41
Mean x= 265.160
41 =6.6 5
Standard deviation
Standard deviation= √ ∑ ¿ ¿ ¿ ¿ ¿
2

Question 2
Descriptive statistics of CGPA is highlighted below.
Question 3
Pie chart for variable ‘Reason’ why students attend university
5%
29%
44%
20%
2%
Reason
1
2
3
4
5
Question 4
The z score for student with graduating CGPA of 7.83
Mean = 6.467
3

Standard deviation = 1.482
z score= x−Mean
Standard deviation
√ Sample ¿ ¿¿ ¿
z score=7.83−6.467
1.482
√41
=5.888
Question 5
The CGPA of 7.83 is significantly different from the mean CGPA at 95% confidence. This
can be concluded as z score corresponding to the CGPA of 7.83 is 5.888 which is
significantly higher than corresponding z value of 95% confidence. It is clearly a outlier as
the corresponding probability associated with the occurrence of this CGPA would be lower
than 0.1% which would not be covered within the 95% confidence interval (Flick, 2015).
Question 6
In order to determine if the given values are significantly different from the sample mean or
not it makes sense to determine the corresponding z value. The requisite computation is
shown below.
z score= 6.5−6.467
1.482
√ 41
=0.14
z score=7−6.467
1.482
√41
=2.30
For a 95% confidence level, the corresponding z values are -1.96 and 1.96. Since the z value
corresponding to the CGPA of 6.5 lies between -1.96 and 1.96, hence it is not significantly
different from the sample mean. However, this is not true for the CGPA of 7 whose
corresponding z score is 2.30 and outside the 95% confidence interval whose z values have
been indicated above as -1.96 and 1.96 (Hillier,2016).
Question 7
Scatter plot of CGPA and Total Hours Studied is shown below.
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