Construct Sample

Question

Construct a sample (with at least two different values in the set) of 4 measurements whose mode is larger than at least 1 of the 5 measurements. If this is not possible, indicate "Cannot create sample".

Answer 1

Trick question. First requirement is to construct a sample of 4 measurements (n = 4)

Second requirement, mode is larger than at least 1 of the 5 measurements (n = 5)

The two requirements are mutually exclusive. No sample possible.

now, if we limited ourselves to an n of 4 and a minimum of 2 values in the set we could construct a set which meets the requirements. {2,3,3,4} is a set with at least 2 different values (3 values in this case), where there is a mode (the mode is 3 which has a density of 2. while the other values have densities of 1.

This set would also have a mean of 3 and a median of 3, as well as a mode of 3 and the mode is greater than at least one of the values.

However, it is a 4 member set so is not allowed. A 5 member would also not be allowed as it dosen't have 4 members.