Let Q = {1.7, 1.1, 1.4, 2.1, 2.3, s}. What is the absolute difference between the greatest and least possible values of the median of set Q? Express your answer as a decimal to the nearest hundredth.
To find the greatest and least possible values of the median, we need to sort the set Q in ascending order.
Sorting the set Q in ascending order:
1.1, 1.4, 1.7, 2.1, 2.3, s
Since we don't know the value of s, we can't determine the exact median. However, we can find the range of possible values for the median.
Let's consider the two cases:
Case 1: s is the smallest value.
In this case, the set Q would be:
s, 1.1, 1.4, 1.7, 2.1, 2.3
The median would be the middle value, which is 1.7.
Case 2: s is the largest value.
In this case, the set Q would be:
1.1, 1.4, 1.7, 2.1, 2.3, s
The median would still be the middle value, which is 2.1.
Thus, the greatest possible value for the median is 2.1, and the least possible value for the median is 1.7.
To find the absolute difference between these values, we subtract the smallest value from the largest value:
2.1 - 1.7 = 0.4
Therefore, the absolute difference between the greatest and least possible values of the median of set Q is 0.4.