What is a set of 5 numbers with a mean 0f 100, a range of 500, and a median of 100.
To find a set of 5 numbers that meets these criteria, we need to consider the properties of mean, range, and median.
1. The mean is the average of all the numbers in a set. In this case, the mean is given as 100. The sum of the numbers divided by 5 should give us a mean of 100. We can use this information to set up an equation: (x1 + x2 + x3 + x4 + x5) / 5 = 100.
2. The range is the difference between the highest and lowest values in a set. Here, the range is given as 500. The range is calculated by subtracting the smallest number from the largest number. So, the largest number - the smallest number = 500.
3. The median is the middle value in a set when it is arranged in ascending or descending order. Given that the median is 100, it means that the third number in our set, when arranged in order, should be 100.
Using these conditions, we can solve for the set of 5 numbers.
Let's assign variables to each number in the set: x1, x2, x3, x4, and x5.
From the equation for the mean: (x1 + x2 + x3 + x4 + x5) / 5 = 100, we can simplify it to:
x1 + x2 + x3 + x4 + x5 = 500
From the equation for the range: largest number - smallest number = 500, we have:
(maximum value) - (minimum value) = 500
Since we know that the median is 100, we can conclude that the third number in the set, when arranged in order, should be 100.
Now we can use trial and error to find a possible set of numbers that satisfy these conditions. We'll start with an example:
Let's assume a set of numbers: 90, 90, 100, 110, and 110.
The mean of this set is: (90 + 90 + 100 + 110 + 110) / 5 = 100 (which satisfies the mean condition).
The range is: (110 - 90) = 20, which does not satisfy the range condition of 500.
Since this set does not meet all the given conditions, we need to keep trying different sets until we find one that satisfies all the conditions.
By continuing this trial and error process, you will eventually find a set of 5 numbers with a mean of 100, a range of 500, and a median of 100.