a data set includes the entries 2, 4, 6, 8, 8, and 11. complete the data set with an entry between 1 and 11…
a data set includes the entries 2, 4, 6, 8, 8, and 11. complete the data set with an entry between 1 and 11 so that the median and mode of the set are equal. (type an integer or decimal)
Answer
Explanation:
Step1: Arrange known data in ascending order
2, 4, 6, 8, 8, 11 There are 6 known data - points. Let the new data - point be (x). The total number of data - points will be (n = 7) (an odd number). For a set with (n = 7) data - points, the median is the (\left(\frac{n + 1}{2}\right))-th value when the data is arranged in ascending order. So the median will be the 4th value.
Step2: Consider cases for mode and median equality
The mode of the current set is 8. If (x\leqslant6), the ordered set is (x,2,4,6,8,8,11), and the median is 6. If (x = 8), the set is (2,4,6,8,8,8,11). The median is 8 (the 4th value when arranged in ascending order), and the mode is 8. If (x\geqslant11), the ordered set is (2,4,6,8,8,11,x), and the median is 8. But we want (x\in[1,11]).
Answer:
8