Final answer:
To find the four integers that have a median of 2.5, a mode of 2, and a range of 3, we can deduce that the list of numbers must include 2 at least twice, a 3 to achieve the median, and a 5 to satisfy the range. Thus, the four integers are 2, 2, 3, and 5.
Step-by-step explanation:
The question asks us to find four integers that have a median of 2.5, a mode of 2 and a range of 3.
First, let's define the terms:
- The median is the middle value in an ordered list of numbers.
- The mode is the number that appears the most frequently.
- The range is the difference between the highest and lowest values in the data set.
Given that the mode is 2, and the median is 2.5, we know that 2 must appear at least twice because modes are the most frequently occurring numbers. Plus, since the median is 2.5, it means that when the four numbers are ordered, the two middle numbers must average to 2.5. Hence, we may have 2 and 3 as the middle numbers since (2 + 3)/2 equals 2.5.
The range is 3, so the difference between the largest and the smallest of our four integers must be 3. Since we already know that one of our numbers must be 2 (the mode), the smallest number could be 2 as well, to adhere to the mode. If the smallest number is 2, to achieve a range of 3, the largest number must be 5.
Therefore, the four integers that meet all the stated criteria are 2, 2, 3, and 5.