Answer :
Final answer:
Out of the statements provided, two must be true: Statement B, which suggests that more than half the temperatures were 88 degrees or higher, and Statement E, which indicates that at least one temperature was exactly 89 degrees.
Explanation:
Based on the information provided about the temperature recordings, we can make conclusions about certain statements:
- Statement A: More than half the recorded temperatures were 89 degrees or higher - This statement cannot be confirmed as true because we only know that 89 is the median, meaning it's just the middle value.
- Statement B: More than half the recorded temperatures were 88 degrees or higher - Must be true, as the mean is 88 degrees which would not be possible if more than half of the values were below 88.
- Statement C: There were no temperatures less than 89 degrees - This is false, the presence of a median of 89 suggests that there must be values both above and below this number.
- Statement D: There were no temperatures less than 88 degrees - This is false, because there must be temperatures both lower and higher than the mean to reach an average of 88.
- Statement E: At least one temperature was exactly 89 degrees - This is true since 89 is the median value in an odd set of temperatures.
- Statement F: At least one temperature was exactly 88 degrees - This cannot be confirmed as true because the mean does not indicate the existence of a specific value, just an average.
Therefore, the statements that must be true are B and E.
