Question

Make up three different data sets with 5 numbers each that have the following characteristics; the word "set" means there will be 2 lists of 5 numbers in each set. List the numbers in each dataset. For example in part a) you will have a list of 5 numbers with a mean of X, and the second list of 5 numbers will have the same mean. However, the two lists of 5 numbers need to have different standard deviations. That is data set #1. For part b, they also need to have the same mean as each other, but they don't have to have the same mean as in part b, although it is ok if they do.

Data set #1: the same mean but different standard deviations.

Data set #2: the same mean but different medians.

Data set #3: the same median but different means.

Answer 1

Data set #1: Here the 2 list of 5 numbers each with the given characteristics could be obtained as:

List A: Here we have all 5 numbers with the mean value of 3 and note that the standard deviation here would be 0 as all the numbers are equal.

List B:

Note that the sum of the 5 numbers above is still 6 + 6 + 3 + 100 - 100 = 15 whose mean has to be 5.

But the standard deviation here is non zero as all 5 numbers are not equal.

Data set #2: Here the 2 list of 5 numbers each with the given characteristics could be obtained as:

We can use the exact same lists as mentioned in the above set.

List A: The mean here is 3 and the median is also 3 as the middle number is 3

List B: Here we arranged the numbers in ascending order and see that the middle number is 6. Therefore the median here is 6 and the mean still remains 3 as computed in the dataset #1 case.

Data set #3: Here the 2 list of 5 numbers each with the given characteristics could be obtained as:

List A: Note that the mean here is still 3 and the median is also 3.

List B: Note that the median still remains the same equal to 3. But the new mean is computed as: (3 + 3 + 3)/ 5 = 1.8

Therefore the two lists here have the same median but different means.