Theory question 105
Data Presentation(a) The frequency table shows the marks scored by 32 students in a test.
Marks scored: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
No. of Students: 2, 3, 4, 4, 4, 4, 5, 3, 2, 1
Find the: (a) (i) Mean (ii) Median (iii) Mode
(b)(i) Find the number of students that scored at least 8 marks. (b) Caculate the percentage that scored at least 8 marks.
Show the model answer
Model answer
(a)(i) Σfx = 2 + 6 + 12 + 16 + 20 + 24 + 35 + 24 + 18 + 10 = 167; mean = 167/32 ≈ 5.2
(ii) Median is the average of the 16th and 17th marks; both are 5, so median = 5
(iii) Mode = 7 (frequency 5)
(b) At least 8 marks: 3 + 2 + 1 = 6 students
Percentage = 6/32 × 100% = 18.75%
Explanation
With 32 values the median is the mean of the 16th and 17th values in order.