| Scores | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 2 | 5 | 13 | 11 | 9 | 10 |
The table shows the distribution of outcomes when a die is thrown 50 times. Calculate the :
(a) Mean deviation of the distribution ; (b) probability that a score selected at random is at least a 4.
Explanation
(a)
| Scores (x) | Frequency (f) | (fx) |
| 1 | 2 | 2 |
| 2 | 5 | 10 |
| 3 | 13 | 39 |
| 4 | 11 | 44 |
| 5 | 9 | 45 |
| 6 | 10 | 60 |
| (sum f = 50) | (sum fx = 200) |
(Mean (bar{x}) = frac{sum fx}{sum f} = frac{200}{50} = 4)
| (d = x – 4) | (|d|) | f | (f|d|) |
| -3 | 3 | 2 | 6 |
| -2 | 2 | 5 | 10 |
| -1 | 1 | 13 | 13 |
| 0 | 0 | 11 | 0 |
| 1 | 1 | 9 | 9 |
| 2 | 2 | 10 | 20 |
| (sum f|d| = 69) |
Hence, Mean Deviation = (frac{sum f|d|}{sum f} = frac{69}{50} )
= (1.38)
(b) Let E denote the event of getting a score of at least 4.
(n(E) = 11 + 9 + 10 = 30)
(p(E) = frac{n(E)}{n(S)} = frac{30}{50})
= (0.6)