The marks obtained by 15 students in a mathematics test are listed below:
68,75,80,62,77,69,85,73,71,78,66,74,72,79,70.
Answer the following questions.
(i) Find the mean mark.
(ii) Prepare a table of (x−xˉ)2 for each observation.
(iii) Using the table, calculate the variance and the standard deviation of the marks.
(iv) If every student is awarded 3 bonus marks, determine the new variance and the new standard deviation.