The daily water usage from a tap was measured. The usage in liters for the first few days are: 5.6, 8, 3.09, 12.9, 6.5, 12.1, 11.3, 20.5, 7.4. (a) Can the mean or median daily usage lie between 25 and 30? Justify your claim using the meaning of mean and median. (b) Can the mean or median be lesser than the minimum value or greater than the maximum value in a data?
No, neither the mean nor the median can lie between 25 and 30. The maximum value in the data is 20.5 liters, and both mean and median must fall within the range of the data values (between minimum and maximum).
No, neither the mean nor the median can be less than the minimum value or greater than the maximum value. The mean is a weighted average of all values within the range. The median is the middle value when sorted, so it must be within or equal to the data values.
Explanation
(a) The mean is an average of all values and must lie within the range of values. The median is the middle value when sorted and must also be within the range. (b) This is a fundamental property of measures of central tendency—they always fall within the range of the data.