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 lower and upper quartiles are not whole numbers.
3. The lower and upper quartiles are not part of the data set.
Hint
What strategy do you use to find the lower/upper quartiles 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, 11, 12}. Here, the lower quartile is 3.5 and the upper quartile is 9.5. You could make this question more challenging by adding more constraints.
Source: Daniel Luevanos
There are many correct answers
the lowest quartile is 7.the high quartile is 13.5
the lower quartile is 3.5 and the upper quartile is 9.5.
Condition 3 follows from conditions 1 and 2.
Also, there are not just many, but infinitely many solutions.
Let n be the number of elements in a data set.
Any data set where n divided by 4 has remainder 0 or 1 and the distance between the elements at the positions floor(n/4) and floor(n/4)+1 is uneven and the distance between the elements at the positions floor(3n/4) and floor(3n/4) + 1 is also uneven fulfills the criteria 1 and 2 and, by extension, criterion 3.
For example:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} or
{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144} or
{1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144} or
{3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 9}