How do you find multiple missing numbers when the mean median and mode is given For Example The mode is 75 the median is 80 and the mean is 85 There are nine numbers in all?

Answer 1

You cannot find the original set, but you can create one set that matches the criteria.

With nine numbers and a median of 80, the 5th number is 80: {x, x, x, x, 80, x, x, x, x}

With a mode of 75, there must be more 75s that any other number. The easiest way to do this is to have two 75s and one of each other number, so the set is now: {x, x, 75, 75, 80, x, x, x, x}.

Finally, with a mean of 85, the easiest way to create nine numbers with such a mean is to split the nine numbers into pairs, one greater than 85 and one less than 85, which together sum to 85 x 2 = 170, and a single number of 85. One such set of nine numbers is {50, 60, 70, 80, 85, 90, 100, 110, 120}. However, there are some previously decided numbers (above), so this set can now be adjusted to accommodate those numbers:

• First, there needs to be two 75s, so increase the first number before 75: it is 70 so increase it to 75 by adding 5, which means that 5 in all must be added to some/all of the numbers after the 85.
• Second, decrease the first number after the 75: it is 80, so decrease it to 75 by subtracting 5, which means that 5 - 5 = 0 must now be added to the numbers after the 85 (ie they can be left alone).
• Third, the median must be 80, but it is currently 85 so reduce it to 80 be subtracting 5, which must be added to the numbers after it.
• Now add the 5 required ensuring that there is no more than one of each number created.

Some sets created:

• {50, 60, 75, 75, 80, 90, 100, 110, 125}
• {50, 60, 75, 75, 80, 93, 101, 111, 120}
• {50, 60, 75, 75, 80, 95, 100, 110, 120}

Staring with another set {70, 75, 80, 82, 85, 88, 90, 95, 100}, the adjustments are: 80 -> 75, 82 -> 78 (less than 80, greater than 75), 85 -> 80 which means there is 5 + 4 + 5 = 14 needed to be added to the right 4 numbers which can lead to the sets:

• {70, 75, 75, 78, 80, 88, 90, 95, 119}
• {70, 75, 75, 78, 80, 91, 94, 97, 105}
• etc