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1. Suppose in a six-team league, the winning percentages were as follows at the end of the season: Team A, 75% ; Team B, 60%; Team C, 50%; Team D, 50%, Team E, 40%, and Team F, 25%. 1. Compute the standard deviation of win percentage based on the formulas in the textbook. 2. Then suppose each team plays a 60-game schedule. Compute the "ideal" benchmark standard deviation of winning percentage based on equal playing strength. 3. Compute the Noll-Scully ratio.

          1. Suppose in a six-team league, the winning percentages were as follows at the end of the season: Team A, 75% ; Team B, 60%; Team C, 50%; Team D, 50%, Team E, 40%, and Team F, 25%.

1. Compute the standard deviation of win percentage based on the formulas in the textbook.

2. Then suppose each team plays a 60-game schedule. Compute the "ideal" benchmark standard deviation of winning percentage based on equal playing strength.

3. Compute the Noll-Scully ratio.
        
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1. Suppose in a six-team league, the winning percentages were as follows at the end of the season: Team A, 75% ; Team B, 60%; Team C, 50%; Team D, 50%, Team E, 40%, and Team F, 25%.

1. Compute the standard deviation of win percentage based on the formulas in the textbook.

2. Then suppose each team plays a 60-game schedule. Compute the "ideal" benchmark standard deviation of winning percentage based on equal playing strength.

3. Compute the Noll-Scully ratio.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Suppose in a six-team league, the winning percentages were as follows at the end of the season: Team A, 75%; Team B, 60%; Team C, 50%; Team D, 50%; Team E, 40%; and Team F, 25%. Compute the standard deviation of win percentage based on the formulas in the textbook. Then suppose each team plays a 60-game schedule. Compute the "ideal" benchmark standard deviation of winning percentage based on equal playing strength. Compute the Noll-Scully ratio.
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Transcript

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00:02 Let's do this question.
00:04 So here, for the part one, the standard deviation for or of winning percentage is equal to square root of summation of x i squared over n minus x bar square over n minus x bar square over n minus 1.
00:43 So from the given data set we have summation x i.
00:48 Square over n is equals to 75 square plus 60 square plus 50 square plus 50 plus 50 square plus 40 square plus 25 square over over 6.
01:12 So this is going to be equals to 2741 .667.
01:22 Now the sample mean x bar is equal to 50 using this data set.
01:27 So our desired standard deviation for winning percentage will be equal to a square root of 27441 .667 minus 50 square over 6 minus 1 so on solving this we have the value 6 .9 522 thus the desired standard deviation is equal to 6 .9 522 now we are moving to the part 2 of this problem so here for 60 games ideal standard aviation is equal to 0 .5 over a square root of x where x we have 60...
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