To find the answer, let's analyze the given information and apply some mathematical reasoning. When talking about a set of data:
- The median is the middle number when the numbers are arranged in order from smallest to largest.
- The range is the difference between the highest and lowest values in the set.
We have 9 construction teams, and the median number of pools installed is 11. Since 9 is an odd number, the median will be the 5th value when we list the pool installation numbers in order. This tells us that there are 4 teams that installed fewer or the same number of pools as the median team, and also 4 teams that installed more or the same number of pools as the median team.
Next, we have a range value of 14. This means that the difference between the team with the most pools installed and the team with the least pools installed is 14.
Since we are trying to find out if the greatest number of pools installed could be 20, let's try to calculate the minimum and maximum number of pools installed by using the given median and range.
Starting with the median at 11, we would have the maximum number at some number X, and the minimum number at some number Y. We need to work out the relationship between these numbers.
The range is X - Y = 14 (since range is the greatest minus the least).
To see if the greatest number could be 20, we can consider the maximum number to be 20 (X = 20) and see if this works with our given values: if Y would still allow the middle value to be 11.
If X is 20, using our range equation X - Y = 14, we can substitute X:
20 - Y = 14
Y = 20 - 14
Y = 6
This means the least number of pools installed would be 6 and the greatest would be 20. Since the median is 11 and falls between these two numbers, this set of numbers would satisfy both the median and range values we are given. Therefore, it is possible that the greatest number of pools installed by any team is 20.
The statement "The greatest number of pools installed could be 20 pools" is true.
Choosing the corresponding answer, it is:
A) True
