Write four different numbers for which both of these statement are true.
-The range is 8
-The mean and median are the same number
-4,4,2,-2
no that is wrong because the range in that is 0 not 8!!!!
To find four different numbers that satisfy both statements, let's start by understanding what the range, mean, and median mean.
1. Range: The range is the difference between the highest and lowest values in a set of numbers. In this case, the range is 8.
2. Mean: The mean is the average of a set of numbers. It is obtained by summing all the numbers and dividing by the count of numbers.
3. Median: The median is the middle value of a set of numbers when they are arranged in numerical order.
Now, let's find four numbers that fulfill both conditions:
To satisfy the condition that the range is 8, we need the numbers to differ by 8 units.
To satisfy the condition that the mean and median are the same number, we need to ensure that the numbers are symmetrically distributed around the same value.
Let's consider an example:
1) Start with the median number, which will also be the mean. Let's choose 10.
2) Now, we need two numbers that are both 8 units away from 10 to satisfy the range condition. We can choose 2 and 18.
3) Finally, we need one more number that is either lower or higher than 10 to complete the set. Let's choose 6.
The four numbers that fulfill both conditions are 2, 6, 10, and 18.
To verify their accuracy, we can calculate the range, mean, and median:
Range: The difference between the highest and lowest number is 18 - 2 = 16, which is 8 as required.
Mean: (2 + 6 + 10 + 18) / 4 = 36 / 4 = 9. The mean is 9, which is also the chosen median.
Median: When arranged in ascending order, the numbers are 2, 6, 10, 18. The middle value is 6, which is equal to the mean.
Therefore, the four numbers that satisfy both conditions are 2, 6, 10, and 18.