Scores 1 2 3 4 5 6 Frequency 2 5 13 11 9 10…

Question 1 Report

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.

Answer

Answer Details

(a) Mean deviation. First find the mean.

Score (x)	1	2	3	4	5	6	Total
Freq (f)	2	5	13	11	9	10	50
fx	2	10	39	44	45	60	200

\[\bar{x} = \frac{200}{50} = 4.0\]

\[\text{Mean deviation} = \frac{\sum f|x-\bar{x}|}{\sum f} = \frac{58}{50} = \mathbf{1.16}\]

(b) Probability of at least a 4. Scores 4, 5 or 6:

\[P(\ge 4) = \frac{11 + 9 + 10}{50} = \frac{30}{50} = \frac{3}{5} = 0.6\]

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 o...