Question

Given the following winning percentages of the teams in a league (for a single year) compute the within-season standard deviation for the league. Team Season Winning Percentage 1 0.750 2 0.750 3 0.200 4 0.600 5 0.200 (a) 0.79 (b) 0.251 (x) 0.56 (d) 0.063

Answer 1

(b) 0.251

Explanation:

1. Standard deviation equation:

`SD=\sqrt{\frac{\sum\limits^N_i {(x_(i)-X)^(2) } }{N} }`

Where X is the mean of the data, and N the amount of data. Then, N=5

2. Estimate the Mean:

`X=(0.750+0.750+0.200+0.600+0.200)/(5)=(2.5)/(5)=0.5\\`

3. Caclulate Standard deviation:

`SD=\sqrt{\frac{{(0.750-0.500)^(2)+(0.750-0.500)^(2)+(0.200-0.500)^(2)+(0.600-0.500)^(2)+(0.200-0.500)^(2) } }{5} }`

`SD=\sqrt{(0.315)/(5) }=√(0.063)\\SD=0.251`