The median number of goals scored by 8 players in a certain soccer season is 5. The range of the number of goals scored by those players that season is 4. Determine if the following statement is true, is false, or does not contain enough information. At least one player scored exactly 5 goals.
NOT ENOUGHT INFO CORECT ANSWER
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To determine if the statement "At least one player scored exactly 5 goals" is true, false, or cannot be determined based on the given information, we need to analyze the data.
We know that the median number of goals scored is 5, which means that when the number of goals is arranged in ascending order, the value in the middle position is 5. Since there are 8 players, the 4th player in the ordered list should have scored 5 goals.
Now, let's consider the range, which is the difference between the maximum and minimum values. The given range is 4, which means the highest scorer's goals minus the lowest scorer's goals is 4. However, with this information alone, we cannot determine the exact values of the highest and lowest scores.
Since we know the median score is 5 and there are 8 players, with the 4th player having scored 5 goals, it is possible for all other players to have scored less than 5 goals or for some players to have scored more than 5 goals.
Therefore, the statement "At least one player scored exactly 5 goals" cannot be determined based on the given information.
False
False.
FALSE?
The scores are
x x x x x x x x
The median is 5, so they are
x x x 5 5 x x x
or
x x x 4 6 x x x
or
3 3 3 3 7 7 7 7
In the first case, 5 goals are scored.
Otherwise, we need not have any scores of 5.