15.9, 15.9, 16, 16, 16.4 is one possible set.
What Five Numbers have a range of 5 a median of 16 and a mean of 15
Median of 16 and 28 is (16+28)/2 = 22
The median of a set of numbers is the middle number when the numbers are listed in numerical order. When there are an even number of data items in the set, then the median is the mean average of the middle two numbers. In the set {16, 25} there are two data items, so the median is the mean average of the middle two (which for a set of 2 is both the numbers) → median = (16 + 25) ÷ 2 = 20.5
7, 11, (16), 18, 23. The median is 16 (shown in brackets).
Mean: 16 Median: 17 Mode: 13 Range: 6
What Five Numbers have a range of 5 a median of 16 and a mean of 15
Mean: 11 Median: 11 Mode: 4 Range: 18
Mean: 50.6 Median: 42 Range: 85 Mode: None (all numbers occur with same frequency)
It is -16, the number halfway between the two middle numbers.
Median of 16 and 28 is (16+28)/2 = 22
There is no direct relationship between the range and the median. So knowing that your median is 20 does not automatically give you the range. The median is just the middle value. That does not tell you what the first and last values are, which is what you need to know to find the range. The median of 19, 20 and 21 is 20, and the range is 2. The median of 4, 20 and 79 is also 20, but the range is 75. The median of 8, 16, 17, 23, 50 and 320 is also 20, but the range is 312. So, as you can see, the Median in no way can tell you what the range will be. You need to know what all of the numbers are, or at least the lowest and highest to know the range.
12, 14, 15, 16, 16, 17 The median is 15.5 The mode is 16 The range is 5 The mean is 15
The median of a set of numbers is the middle number when the numbers are listed in numerical order. When there are an even number of data items in the set, then the median is the mean average of the middle two numbers. In the set {16, 25} there are two data items, so the median is the mean average of the middle two (which for a set of 2 is both the numbers) → median = (16 + 25) ÷ 2 = 20.5
7, 11, (16), 18, 23. The median is 16 (shown in brackets).
Assuming that you want to discount luck (if not, the answer would be 1), and that the guesser always guesses the median of the remaining range, the answer would be the (ceiling of the log(base 2) of the count of numbers in the range). If the log(base 2) is an exact integer, add 1. Example 1, pick a number between 1 and 9. There are 9 numbers in the range, so the log(base2) of 9 is ~3.16. The ceiling of that is 4. Do not add 1 for a final answer of 4. The full range is 1,2,3,4,5,6,7,8,9. The median is 5 First guess is 5. Higher - 6,7,8,9 is remaining range. 7 and 8 are the median numbers Second Guess is 8. Lower - 6,7 is the remaining range. 6 and 7 are the median numbers. Third guess is 7. Lower - 6 is the remaining range. 6 is the median number Fourth guess is 6. Correct. Example 2, pick a number between 1 and 16. There are 16 numbers in the range, so the log(base 2) of 16 is 4. The ceiling of 4 is 4. Add the 1 because the Log(base 2) is an integer, for a final answer of 5. Full range is 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16. The median numbers are 8 and 9. First Guess is 9. Lower - 1,2,3,4,5,6,7,8 is the remaining range. 4 and 5 are the median numbers Second Guess is 4. Higher - 5,6,7,8 is the remaining range. 6 and 7 are the median numbers. Third Guess is 6. Higher - 7,8 is the remaining range. 7 and 8 are the median numbers. Fourth Guess is 7. Higher - 8 is the remaining range. 8 is the median. Fifth guess is 8. Correct Both of these examples show worst case scenarios. A "lucky guess" will reduce the number of guess needed, possibly all the way to 1. Note: I do realize that to a math purist, in the examples where I said that the median numbers were x and y, the correct answer is that the median number is between x and y. Since I can not guess the number between the two numbers, I am bending the definition of median to treat the two bordering numbers as the median when the strict definition would list the median as being between those two numbers.
16.5 is the median. A median is the middle number of a set of numbers in order. If there are an even amount of numbers, as in this case, it is the number half way between the two middle numbers, in this case 16 and 17.
The numbers are, 12 13 16 17 17