The average (arithmetic mean) daily temperature for a week was recorded for two different cities. Each city had 7 days of temperature data.
City R: Mean daily temperature of 68°F
City S: Mean daily temperature of 62°F

Which of the following MUST be true?
I. The highest daily temperature recorded in City S was lower than the lowest daily temperature recorded in City R.
II. The median daily temperature in City R was higher than the median daily temperature in City S.
III. There was at least one day in City R when the temperature was higher than the temperature on at least one day in City S.