The raw scores of 20 students of Utopia High School who took part in an examination in Economics are given below. The pass mark is 40%
38 28 70 43
39 20 64 66
12 46 52 53
20 34 48 69
18 20 64 34
(a) What is the mean score of the students’ marks?
(b) How many students passed the examination?
(c) What percentage of the students failed the examination?
(d) What is the range of the scores?
(e) How many students scored below the mean score?
Explanation
| Marks (x) | Frequency (f) | fx |
| 12 | 1 | 12 |
| 18 | 1 | 18 |
| 20 | 3 | 60 |
| 28 | 1 | 28 |
| 34 | 2 | 68 |
| 38 | 1 | 38 |
| 39 | 1 | 39 |
| 43 | 1 | 43 |
| 46 | 1 | 46 |
| 48 | 1 | 48 |
| 52 | 1 | 52 |
| 53 | 1 | 53 |
| 64 | 2 | 128 |
| 66 | 1 | 66 |
| 69 | 1 | 69 |
| 70 | 1 | 70 |
| 838 | 20 | 838 |
(a) Mean = \(\frac{\sum fx}{\sum f}\)
= \(\frac{828}{20}\) = 41.9
(b) 10 students
(c) Percentage of students that failed the examination
=\(\frac{10}{20} \times \frac{100}{1}\)
(d) Range of the score is 70 - 12 = 58
(e) 10 students scored below the mean score.