Answer:
(a) The mean is 24
The Absolute deviation is 8.367
(b) Mean is the number of score per game
(b) The standard deviation is the normal expected score difference from the mean
(c) Mean reduce
Standard deviation reduce
Explanation:
The data is as follows;
21, 45, 21, 14, 21, 28, 24, 14, 24, 28
The data with n = 10 is presented as follows
x (x - μ) (x - μ)²
21 -3 9
45 21 441
21 -3 9
14 -10 100
21 -3 9
28 4 16
24 0 0
14 -10 100
24 0 0
28 4 16
∑x/n =240 ∑(x - μ)² = 700
24 ∑(x - μ)²/n = σ² = 70
The mean = 24
The Absolute deviation √70 = 8.367
(b) The mean indicates that within the football season, the average game score per game was 24 and the normal variation from the average was 8.367
(c) Removing the outlier, 45 which ls most equal to two means will reduce the mean or average score per game of the team to as follows
21 , 21 , 14, 21, 28, 24, 14, 24, 28
∑x = 195 and μ = (∑x)/n = 195/9 = 21.67
The standard deviation = 4.83
Therefore, removing the outlier 45 which is almost double the mean will reduce the mean by almost μ/n and the standard deviation is also reduced.