Final answer:
To calculate percentiles, order the data from least to greatest, find the position by multiplying the number of scores by the desired percentile, and round the position to the nearest whole number. The percentiles for the team with 91 wins are: 60th percentile: 91 wins, 70th percentile: 97 wins, 80th percentile: 99 wins, 90th percentile: 100 wins.
Step-by-step explanation:
The percentile of a particular score can be found by determining the percentage of scores that fall below that score. To calculate percentiles:
- Order the data from least to greatest.
- Find the position (P) of the score by multiplying the number of scores (N) by the desired percentile (P/100).
- Round P to the nearest whole number. If P is a whole number, the percentile is the average of the values at positions P and P+1. If P is not a whole number, round up to the nearest whole number and the percentile is the value at that position.
To find the percentiles for the team with 91 wins:
- Order the number of wins from least to greatest.
- Calculate the positions:
- 60th percentile: N * (60/100) = 30 * 0.6 = 18
- 70th percentile: N * (70/100) = 30 * 0.7 = 21
- 80th percentile: N * (80/100) = 30 * 0.8 = 24
- 90th percentile: N * (90/100) = 30 * 0.9 = 27
- Round the positions:
- 60th percentile: P = 18
- 70th percentile: P = 21
- 80th percentile: P = 24
- 90th percentile: P = 27
- Find the values at the rounded positions:
- 60th percentile: 91 wins
- 70th percentile: 97 wins
- 80th percentile: 99 wins
- 90th percentile: 100 wins
Interpretation:
- 60th percentile: 60% of the teams had 91 or fewer wins
- 70th percentile: 70% of the teams had 97 or fewer wins
- 80th percentile: 80% of the teams had 99 or fewer wins
- 90th percentile: 90% of the teams had 100 or fewer wins