Open Middle®
Directions: Create a statistical data set of at least 10 numbers such that:
1. All of the numbers in the data set are whole numbers.
2. The median is not a whole number.
3. The median is not part of the data set.
Hint
What strategy do you use to find the median of a data set? Does this strategy work in all cases?
Answer
There are many correct answers. One statistical data set that would work is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Here the median is 5.5. You could make this question more challenging by adding more constraints.
Source: Daniel Luevanos
1,2,3,4,5,6,7,8,9,10
The median would be 5.5, it is not in the data set nor a while number
10,11,12,13,14,15,16,17,18,19.
The median would be 14.5 which which is not in the data set or a whole number.
1,2,3,4,5,6,7,8,9,10
The median is 5.5 which is NOT part of the data set or a whole number.
You could do 1,2,3,4,5,6,7,8,9,10. This is because the median is 5.5. That number is not in the data set. The number also is not a whole number. Another combo could be 30,31,32,33,34,35,36,37,38,39. The median is 35.5 which is not a whole number. It also is not in the data set.
1,2,3,4,5,6,7,8,9,10
1,2.3.4 the median is 2.5
1,2,3,4,5,6,7,8,9,10
The median would be 5.5, it is not in the data set nor a while number
4,9,10,1. The median would be 9.5 which is not a whole number nor a number in the data set.
10,12,14,16,18,20,22,24,26,28. The Mean is 19
What is the median 1, 2, 3, 4 , 5, 6, 7, 8, 9, 10?
I think the median is 5.5 because the medium is 5 plus .5 is 5.5
Condition 3 follows automatically from 1 and 2. If all elements in the set have to be whole numbers and the median is not a whole number, then of course it’s not in the data set.
And there are not just many correct answers, but infinitely many. Any data set of whole numbers with an even amount of elements, where the distance between the middle two elements (of the ordered set) is uneven fulfills conditions 1 and 2 and, by extension, condition 3.
For example, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} has an even amount of elements and the distance between the middle two elements is 1, an uneven number, which is why it works. Other solutions include:
{1, 1, 2, 3, 5, 8, 13, 21, 34, 55}
{1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
{3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9}