What are 10 numbers that have a median of 21, a range of 20, and a mode of 10?
10,10,10,10,21,21,22,23,24,30
u have lots of answers
10
To find 10 numbers that meet these criteria, we can follow a step-by-step approach:
Step 1: Let's determine the range of the numbers. The range is the difference between the largest and smallest values. In this case, the range is given as 20.
Step 2: Since the mode is given as 10, it means that at least two numbers in the list must be 10.
Step 3: Now let's consider the median value. Since we have an even number of values (10 in total), the median will be the mean of the middle two values.
Step 4: Since the range is 20, the largest value must be the median plus 10 (half of the range), and the smallest value must be the median minus 10.
Step 5: Let's assume that the two numbers that are equal to 10 are at the beginning of the list, so we start with 10, 10.
Step 6: Since we know the median is 21, the two middle values should average to 21. Let's use variables to represent these values: x and y.
The 10 numbers can be written as: 10, 10, x, y, _, _, _, _, _, _
Step 7: To satisfy the median condition, we can set the value of x to 21 and y to 31 (because 21 + 31 divided by 2 gives us the median of 21).
The 10 numbers now become: 10, 10, 21, 31, _, _, _, _, _, _
Step 8: Now, we need to distribute the remaining six numbers. Since they should have a range of 20, we can divide the range equally. We add 10 to the smallest number, and subtract 10 from the largest number.
The final set of 10 numbers with the given conditions is: 10, 10, 21, 31, 11, 12, 13, 14, 30, 32.
Verifying our solution:
- Range: The largest number (32) minus the smallest number (10) equals 22, which is the desired range of 20.
- Median: The middle two numbers are 21 and 31, which average to 26. This matches the desired median of 21.
- Mode: The number 10 appears twice in the list, so the mode is indeed 10.
Therefore, the 10 numbers are 10, 10, 21, 31, 11, 12, 13, 14, 30, 32.