The table below gives the frequency distribution of the marks obtained by some students in a scholarship examination.
| Scores (x) | 15 | 25 | 35 | 45 | 55 | 65 | 75 |
| Freq (f) | 1 | 4 | 12 | 24 | 18 | 8 | 3 |
(a) Calculate, correct to 3 significant figures, the mean mark.
(b) Find the : (i) mode ; (ii) range of the distribution.
Explanation
(a)
| x | f | fx |
| 15 | 1 | 15 |
| 25 | 4 | 100 |
| 35 | 12 | 420 |
| 45 | 24 | 1080 |
| 55 | 18 | 990 |
| 65 | 8 | 520 |
| 75 | 3 | 225 |
| | 70 | 3350 |
\(Mean = \frac{\sum fx}{\sum f} = \frac{3350}{70} = 47.8571\)
\(\approxeq 47.9\) (to 3 sig. figs)
(b)(i) Mode = 45 (score with the highest frequency)
(ii) Range = Highest mark - Lowest mark
= 75 - 15 = 60.
