Theory question 108
Data PresentationThe marks scored by 50 students in a Geography examination are as follows:
60 54 40 67 53 73 37 55 62 43
44 69 39 32 45 58 48 67 39 51
46 59 40 52 61 48 23 60 59 47
65 58 74 47 40 59 68 51 50 50
71 51 26 36 38 70 46 40 51 42
(a) Using class intervals 21 − 30, 31 − 40, …, prepare a frequency distribution table.
(b) Calculate the mean mark of the distribution.
(c) What percentage of the students scored more than 60%?
Show the model answer
Model answer
(a) 21–30: 2; 31–40: 10; 41–50: 12; 51–60: 15; 61–70: 8; 71–80: 3 (total 50).
(b) Class marks 25.5, 35.5, 45.5, 55.5, 65.5, 75.5: Σfx = 51 + 355 + 546 + 832.5 + 524 + 226.5 = 2535. Mean = 2535/50 = 50.7.
(c) Marks above 60: 11 students (from the list). 11/50 × 100% = 22%.
Explanation
Check the frequencies add up to 50 before working out the mean.