Three different numbers have median 2 and range 2. Find the three numbers
1 2 3
0.1 2 2.1
1.9 2 3.9
Just pick any two numbers that differ by 2; one above 2 and one below.
Well, to find the three numbers, we should start by looking at the range being 2. Let's assume the smallest number is x. That means the largest number would be x + 2, since the range is 2.
Now, let's think about the median being 2. If we have three numbers sorted in ascending order, the median would be the middle number. Since the median is 2, the middle number would be 2.
So, our three numbers would be x, 2, and x + 2. And their median would indeed be 2 and the range would be 2. Voila!
Let's solve this step-by-step:
Step 1: Find the middle number (median):
Since the median is given as 2, the middle number is 2.
Step 2: Find the range:
The range is defined as the difference between the largest and smallest numbers. In this case, the range is 2.
Step 3: Find the largest number:
Since the range is 2, and we know the middle number is 2, the largest number would be 2 + 1 = 3.
Step 4: Find the smallest number:
To find the smallest number, we subtract the range from the middle number. In this case, the smallest number would be 2 - 1 = 1.
Step 5: Find the three numbers:
Using the information above, we have found that the median is 2, the largest number is 3, and the smallest number is 1. Therefore, the three numbers are 1, 2, and 3.
To find the three numbers, we need to consider the given information: the median is 2, and the range is 2.
Let's start by understanding what the median represents. The median is the middle value in a set of numbers when arranged in order. Since the median is 2, it means that one of the numbers is exactly 2.
Next, we know that the range is 2. The range is the difference between the highest and lowest values in a set of numbers. In this case, the difference between the highest and lowest numbers is 2.
Now let's consider the different possibilities for the three numbers:
1. Scenario 1: If the numbers are evenly spaced, the lowest number would be 2 - 1 = 1, and the highest number would be 2 + 1 = 3. That would give us the set {1, 2, 3}.
2. Scenario 2: If the numbers are not evenly spaced, we can have a middle number that is 2 and find the minimum and maximum values accordingly. For example, let the minimum value be x and the maximum value be y. Since the range is 2, we have two cases to consider:
a) If x is less than 2, then y = 2 + (range/2) = 2 + (2/2) = 3. So, the set would be {x, 2, 3}.
b) If x is greater than 2, then y = 2 - (range/2) = 2 - (2/2) = 1. So, the set would be {1, 2, x}.
It is important to note that multiple sets can fulfill the given conditions depending on the specific values of x and y. However, we have provided the general approach to finding the three numbers based on the information given.