Question

Think of 5 positive integers that have a mode of 2 and 5, a median of 5 and a mean of 5.

Answer 1

S = {2, 2, 5, 5, 11}

Explanation:

So you can partially build a data set given this information. There is going to be 5 positive numbers and the median is going to be 5 so the data set is going to have 5 in the middle which should look like this

S = {a, b, 5, c, d} where a, b, c, d are the other values. Since it has a mode of 2 and 5 that means that the occurrences of 2 and 5 will be equal, otherwise it would only have 1 mode. and they have to appear at least twice since if they only appeared once, there would either be another mode, or the data set would have 5 modes.

So the data set is going to look like this

S = {2, 2, 5, 5, d}

Now the only thing left to do is calculate d. This is where you use the mean to determine the last value. The mean can be calculated as

(the sum of the data set) / (the amount of values in the data set)

Since we know the mean you can set up an equation to find the value of d

`5 = (2+2+5+5+d)/(5)\\5=(14+d)/(5)\\25=14+d\\11=d`

so the last value is 11. This gives you the complete data set of 5 positive integers

S = {2, 2, 5, 5, 11}