For many, statistics and probability are the most fun aspects of mathematics. These two related sub categories involve much more of the doing that can make math interesting and fun. Statistics are used in every day life. Probability is appreciated by those who enjoy games. Both of these can become so advanced that they become difficult, and those who are experts with them can use them to predict outcomes. For example, television news outlets use statistical and probability experts during presidential elections to predict the outcomes for states based on a small percentage of the reporting population.
Statistics focuses on the analysis of collected data. There are many things one can do with this collected data. Some of the most frequently used are the measures of central tendency. These are the mean, median and mode. (Also the first and third quartile.) The mean is the average value of the data. The median is the middle term when all are listed from lowest to highest. The mode is the piece that appears most often. Statistics can become more complicated when ideas like variance and standard deviation are introduced. Using these, statisticians can then create bell curves and normalized data charts.
On the simpler side of statistics, people can use collected data to create bar graphs, line graphs, and pie charts. These are great visual tools which illustrate the magnitude of the collected data, and are particularly appropriate for various presentations.
Probability is all about determining likelihood of outcomes. An event happens, such as a toss of a coin, and mathematicians are able to determine the likelihood of landing heads up. These too get much more complicated, and involve dependent or independent events, and so much more. Most principals of probability have to do with dice and cards. Here is a fun fact about about probability. There is something known as, “Gambler’s Fallacy.” It has to do with streaks. The idea is that the outcome of previous independent events have no bearing on the probability of the next one. If a fair coin is flipped four times, and it is a tails every time, it is just as likely to be a tails the fifth time as it is to be a heads. Therefore, the idea, “heads is due to come up” is a fallacy.