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

Answer:

(b) 0.251

Step-by-step 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:

$X=\frac{0.750+0.750+0.200+0.600+0.200}{5}=\frac{2.5}{5}=0.5$

3. Caclulate Standard deviation:

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

$SD=\sqrt{\frac{0.315}{5} }=\sqrt{0.063}\\SD=0.251$