Discrete Mathematics
# Understanding Data

What is wrong with this news coverage?

There are eight people in a family. One of the members receives \(x\) presents. Five members receive \(x+4\) each and the rest only get \(x-2\) each.

Consider the 8 numbers of presents received, and find \[2 \times \mathrm{mode} - \mathrm{mean} - \mathrm{median}.\]

The sum of \(N\) real numbers (not necessarily unique) is 20. The sum of the 3 smallest of these numbers is 5. The sum of the 3 largest is 7. Which of the following are possible values for \(N\)?

I. 9

II. 10

III. 11

The value of \(x\) is the mean of the numbers in the white circles. The values of \(y\) is the mean of numbers in the blue circles.

Find \(x-y\).

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