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25 Sep 2025, 04:11
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The median points per game of All-Star players is greater than the maximum points per game of non-All-Star players.: Yes
The mode of assists is greater than the range of assists.: No
Points and turnovers are directly proportional to each other.: No
The table displays performance data per season for selected professional basketball players: whether they are on the All-Star roster, field goal percentage, points per game, rebounds per game, assists per game, steals per game, blocks per game, and turnovers per game.
For each of the following statements, select Yes if the statement is true based on the information provided; otherwise select No.
| Player | All-Star (yes/no) | FG% | Points | Rebounds | Assists | Steals | Blocks | Turnovers |
|---|---|---|---|---|---|---|---|---|
| Adams | yes | 51 | 24 | 9 | 4 | 2 | 1 | 3.1 |
| Barker | no | 46 | 18 | 6 | 5 | 1 | 0 | 2.5 |
| Chang | yes | 54 | 27 | 10 | 6 | 2 | 1 | 3.4 |
| Diaz | no | 44 | 15 | 5 | 3 | 1 | 0 | 2.1 |
| Ellis | yes | 48 | 20 | 7 | 5 | 1 | 0 | 2.7 |
| Foster | yes | 55 | 22 | 11 | 4 | 2 | 1 | 3.0 |
| Garcia | no | 42 | 13 | 6 | 2 | 1 | 0 | 1.9 |
| Hayes | yes | 50 | 19 | 8 | 5 | 1 | 1 | 2.6 |
| Inoue | yes | 53 | 26 | 12 | 7 | 2 | 1 | 3.5 |
| Johnson | yes | 47 | 21 | 7 | 6 | 1 | 0 | 2.8 |
| Kim | no | 45 | 16 | 5 | 4 | 1 | 0 | 2.2 |
| Lopez | no | 41 | 12 | 6 | 2 | 1 | 0 | 1.8 |
| Martins | yes | 52 | 25 | 9 | 6 | 2 | 1 | 3.3 |
| Nash | no | 43 | 14 | 5 | 3 | 1 | 0 | 2.0 |
| Owens | yes | 49 | 23 | 8 | 5 | 1 | 1 | 3.0 |
For each of the following statements, select Yes if the statement is true based on the information provided; otherwise select No.
| Yes | No | |
| The median points per game of All-Star players is greater than the maximum points per game of non-All-Star players. | ||
| The mode of assists is greater than the range of assists. | ||
| Points and turnovers are directly proportional to each other. |
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Official Answer
The median points per game of All-Star players is greater than the maximum points per game of non-All-Star players.: Yes
The mode of assists is greater than the range of assists.: No
Points and turnovers are directly proportional to each other.: No
25 Sep 2025, 04:11
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Official Solution:
• The median points per game of All-Star players is greater than the maximum points per game of non-All-Star players.
The All-Star point values are 24, 27, 20, 22, 19, 26, 21, 25, and 23. When ordered from least to greatest they are 19, 20, 21, 22, 23, 24, 25, 26, 27, giving a median of 23. The non-All-Star point values are 18, 15, 13, 16, 12, and 14, with a maximum of 18. Since 23 is greater than 18, the statement is true.
Answer: Yes
• The mode of assists is greater than the range of assists.
Mode means the most frequent value, and range means the difference between the highest and lowest value. Checking the column, the mode is 5 because it appears the most frequently (4 times). The range is 7 − 2 = 5. Since the mode is equal to the range, not greater, the statement is false.
Answer: No
• Points and turnovers are directly proportional to each other.
Directly proportional means the ratio of points to turnovers should be constant across the players. The ratios vary widely, for example Chang has 27/3.4 ≈ 7.9, while Lopez has 12/1.8 ≈ 6.7. Since the ratios are not constant, the statement is false.
Answer: No
Correct answer:
The median points per game of All-Star players is greater than the maximum points per game of non-All-Star players. "Yes"
The mode of assists is greater than the range of assists. "No"
Points and turnovers are directly proportional to each other. "No"
bb
• The median points per game of All-Star players is greater than the maximum points per game of non-All-Star players.
The All-Star point values are 24, 27, 20, 22, 19, 26, 21, 25, and 23. When ordered from least to greatest they are 19, 20, 21, 22, 23, 24, 25, 26, 27, giving a median of 23. The non-All-Star point values are 18, 15, 13, 16, 12, and 14, with a maximum of 18. Since 23 is greater than 18, the statement is true.
Answer: Yes
• The mode of assists is greater than the range of assists.
Mode means the most frequent value, and range means the difference between the highest and lowest value. Checking the column, the mode is 5 because it appears the most frequently (4 times). The range is 7 − 2 = 5. Since the mode is equal to the range, not greater, the statement is false.
Answer: No
• Points and turnovers are directly proportional to each other.
Directly proportional means the ratio of points to turnovers should be constant across the players. The ratios vary widely, for example Chang has 27/3.4 ≈ 7.9, while Lopez has 12/1.8 ≈ 6.7. Since the ratios are not constant, the statement is false.
Answer: No
Correct answer:
The median points per game of All-Star players is greater than the maximum points per game of non-All-Star players. "Yes"
The mode of assists is greater than the range of assists. "No"
Points and turnovers are directly proportional to each other. "No"
30 Oct 2025, 12:15
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I did not quite understand the solution. Why are we considering the ratio? If we look at the table, we can clearly see that the points and turnover are increasing in proportion. Can you please help with this solution?
