If a set of data has 5 numbers a mean of 9 median of 6 and a mode of 6 what are the five numbers?

Answer 1

Let this data be a, b, c, d, and h.
Since the median is 6, then c = 6.
Since the mean of the five data is 9, that is the sum of the data values is 45 (an odd number).
Since the mode is 6, that means at least two of the data values are 6.
Since the sum of the data is an odd number, we must have only two data values of 6 (even), and the three other numbers must be odd numbers. Thus, b or d could be 6.

Therefore, the sum of the three odd numbers is 33.

If the data are a b 6 6 h, a and b could be 1 and 3, 1 and 5, or 3 and 5. So that h could be 25, 27, or 29.

Thus, the data could be:

1 3 6 6 29 or 1 5 6 6 27 or 3 5 6 6 25.

If the data are a 6 6 d h, a could be 1, 3, or 5. So that the data could be:

1 6 6 7 25 or 1 6 6 9 23 or 1 6 6 11 21 or 1 6 6 13 19 or 1 6 6 15 17

3 6 6 7 23 or 3 6 6 9 21 or 3 6 6 11 19 or 3 6 6 13 17

5 6 6 7 21 or 5 6 6 9 19 or 5 6 6 11 17 or 5 6 6 13 15