I found these solutions by using a base set and changing numbers to satisfy the desired values.
Q. 1: Can you find other sets of five numbers where:
Mean = Median = Mode = Range
4,10,10,12,14
6,15,15,18,21
Q. 2: Can you find sets of five numbers that satisfy the following properties?
A. Mode < Median < Mean
1,1,4,10,14
Mode = 1, Median = 4,Mean = 6
B. Mode < Mean < Median
2,2,9,10,12
Mode =2 , Median =9 ,Mean =7
C. Mean < Mode < Median
Mode = , Median = ,Mean =
Not possible. Explained later.
D. Mean < Median < Mode
https://docs.google.com/document/u/2/d/1hNxwiQwlFKM0TFIb3eOxMbh9mO6Q02m… 3/27/26, 8:08 AM
Page 1 of 22,5,8,10,10
Mode = 10,Median = 8,Mean = 6
E. Median < Mode < Mean
5,10,15,40,40
Mode = 40 , Median =15 ,Mean = 22
F. Median < Mean < Mode
Q.3 : Not all of these can be satisfied by sets of five numbers! Can you explain why
F:since they can only be accomplished with the median being a decimal, not
a whole number.
2C: since the smallest target should be 20.then it should average out to 4 in
each place.Since the numbers have to be smaller than 4, making the median
will not be possible.
Q.4: Show that some of them can be satisfied with sets of just four numbers.
A 1,1,3,9 B.2,2,10,4.
Q. 5: Show that all of them can be satisfied with sets of six numbers.
A 1,1,5,5,10,33
B 3,3,10,10, 20,
C 0,1,2,7,9,9.
D 2,3,6,10,10,11
I can not find any answers for F and E