Learn the basic statistical measures - Assignment 11

 

Problem : Study Habits and Examination Performance

Problem Statement

A teacher wants to investigate whether students' study habits are related to their examination performance. The following data were collected from 10 students.

Student    Study Hours/Week    Exam Marks
S1    8        55
S2    10    60
S3    12    65
S4    15    70
S5    16    72
S6    18    78
S7    20    80
S8    22    85
S9    25    88
S10    28    92

Tasks

Students should:

  1. Create a data frame containing the above data.
  2. For Study Hours and Exam Marks, calculate:
    • Mean
    • Median
    • Mode
  3. Calculate measures of variability:
    • Range
    • Variance
    • Standard deviation
    • Interquartile range (IQR)
  4. Calculate the covariance between Study Hours and Exam Marks.
  5. Calculate the Pearson correlation coefficient between Study Hours and Exam Marks.
  6. Draw a scatter plot of Study Hours versus Exam Marks.
  7. Box plot of Study Hours and Exam Marks.
  8. Interpret the covariance and correlation.
  9. Based on the results, comment on whether students who study more hours tend to obtain higher marks.

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