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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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
\(\sum f|d| = 58\)
Hence, Mean Deviation = \(\frac{\sum f|d|}{\sum f} = \frac{58}{50}\)
= 1.16
(b) Let E denote the event of getting a score of at least 4.
\(n(E) = 11 + 9 + 10 = 30\)
\(p(E) = \frac{n(E)}{n(S)} = \frac{30}{50}\)
= \(0.6\)
Source: Myschool Past Questions Archive (Record #52635)