Analysis of Student Marks and Preparation Time: Survey Results, Histograms, Scatter Plot, and Descriptive Statistics

HOLMES INSTITUTE
FACULTY OF HIGHER EDUCATION
HI6007 Group Assignment
Due End of Week/Lecture 10
WORTH 30%
Please read below information carefully and respond all questions listed.
Page 1

1. Many Holmes Institute instructors believe that students need to spend at least 2 hours
studying outside of class for every hour of lecture. They believe that the number of hours
students study to prepare for the exam affect students’ marks significantly. As opposed,
few of the lecturers believe that the number of preparation hours do not essentially affect
students’ marks while some other factors are to be considered. To study the relationship
between the preparation time spent by each student (in hours) for the exam and the
reported mark, a sample of 100 students were selected randomly from a large statistics
class. The data are stored in the file named “ASSIGNMENTDATA” in the course website.
Answer below 9 questions:
a. What type of survey method could be used? Explain your answer.
Answer
Cross-sectional survey; this is where the researcher collects data from the
respondents at a single period in time uses the cross-sectional type of survey.
b. What sampling method could be used to select the sample? Explain your answer.
Answer
Simple random sampling could be used. This method would give the participants an
equal chance of being included into the study and as such will reduce the chances
of bias.
c. On the basis of given data, determine the dependent and independent variables we
should use, and why? Also, identify the data type(s) for each variable.
Answer
The dependent variable is the student’s marks while the independent variable is the
number of hours students study to prepare for the exam. This is because number of
hours students study to prepare for the exam is believed to influence the students
marks hence it is the independent variable while the student marks is the
dependent variable.
d. What kind of issues we may face in collecting the data using this type of survey
method? List and explain two cases.
Answer
Some of the issues that might be faced include;
 Non-response from some of the participants. Some participants might not
be willing to respond for their own reasons.
Page 2

 High cost of collecting data; one challenge would be in regard to the cost if
the participants are widely spread apart.
e. Using 8 classes and intervals of 20 - 30, 30 - 40, etc for both of the variables
selected in question 3, develop a distribution table including class intervals,
frequency, relative frequency and cumulative relative frequency for each variable.
Then, draw frequency histogram, relative frequency histogram and cumulative
relative frequency histogram for each variable. Also, Comment on the shape of
frequency histogram for each variable and provide reason(s) for your comment.
Answer
Table 1 Distribution table for preparation time
Class
Interval
Frequency Relative
Frequency
Cumulative relative
frequency
20-30 1 0.01 0.01
30-40 8 0.08 0.09
40-50 16 0.16 0.25
50-60 20 0.2 0.45
60-70 20 0.2 0.65
70-80 17 0.17 0.82
80-90 12 0.12 0.94
90-100 6 0.06 1
Table 2: Distribution table for student marks
Class
Interval
Frequency Relative
Frequency
Cumulative relative
frequency
20-30 1 0.01 0.01
30-40 5 0.05 0.06
40-50 10 0.1 0.16
50-60 17 0.17 0.33
60-70 21 0.21 0.54
70-80 22 0.22 0.76
80-90 14 0.14 0.9
90-100 10 0.1 1
Histograms for the preparation time
Page 3