The five number summary combines five descriptive statistics to give us a fuller picture than what we might have by just looking at one of these numbers. The five numbers used are the minimum, maximum, median, and first and third quartiles. A boxplot can be used to give a graphical display of a five number summary.

A paradox is a statement or situation that seems contradictory on the surface, but may reveal some underlying truth. Paradoxes abound throughout different disciplines. A few of the ones that deal with areas connected to probability and statistics are:

• The Barber Paradox - this paradox goes to the foundations of mathematics, and what the defintion of set means
• The St. Petersburg Paradox - shows that an analysis of a game should involve more than just the calculation of an expected value.
• Simpson's Paradox - reveals some of the problems that arise when we lump too much data together.

A standard probability problem involves the rolling of two dice, and calculating the probabilities. But what about three dice?

Calculating probabilities for three dice is a trickier problem due to a couple of factors. Rather than 36 different possibilities with two dice, there are 216 for three. Also, there are a number of different ways to use three dice to form the same sum. For example, 6 = 1+2+3=2+2+2=1+1+4, as well as varying permutations of these sums.

The chi-square statistic is an important tool to quantify how much an observed value in a statistical experiment varies from an expected value. The expected values are typically calculated using probability or some mathematical model. Chi-square tests are used in two-way tables or multinomial experiments

The formula to calculate the chi-square statistic is not very complicated. There are actually less steps for the chi-square formula than for the formula for standard deviation.