High School

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Justin recorded the temperature outside at 4:00 p.m. for 9 days straight. Each day had a different recorded temperature.

- The mean temperature was 88.
- The median temperature was 89.

Based on this information, select all the statements that must be true:

A. More than half the recorded temperatures were 89 degrees or higher.
B. More than half the recorded temperatures were 88 degrees or higher.
C. There were no temperatures less than 89 degrees.
D. There were no temperatures less than 88 degrees.
E. At least one temperature was exactly 89 degrees.
F. At least one temperature was exactly 88 degrees.

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.

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