The 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%?
Explanation
(a)
| Marks | frequency | mid-point | \(fx\) |
| 21 - 30 | 2 | 25.5 | 51 |
| 31 - 40 | 10 | 35.5 | 355 |
| 41 - 50 | 12 | 45.5 | 546 |
| 51 - 60 | 15 | 55.5 | 832.5 |
| 61 - 70 | 8 | 65.5 | 524 |
| 71 - 80 | 3 | 75.5 | 226.5 |
| \(\sum\) | 50 | 2535 |
(b) Mean (x) = \(\frac{\sum fx}{\sum f}\)
= \(\frac{2535}{50}\)
= \(50.7\)
(c) Number of students that scored above 60% : 8 + 3 = 11
%age : \(\frac{11}{50} \times 100% = 22%\)