The table below shows the distribution of marks (out of 100) obtained by 60 students in a unit test.
Marks (class interval) Number of students
0 – 20 7
20 – 40 12
40 – 60 ?
60 – 80 15
80 – 100 8
Answer the following questions.
(i) Determine the missing class frequency so that the total number of students is 60.
(ii) Calculate the arithmetic mean of the marks obtained by the students.
(iii) Hence find the variance and the standard deviation of the marks (correct to two decimal places).