BASIC STATISTICS

By Osman Sencan

The Origins of Probability Theory

Since gambling in the ancient times, people had the notion of probability. In the seventieth century, this probability theory increased by the mathematicians Blaise Pascal and Pierre de Fermat. Now it helps us with risk assessments such as in the insurance industry, in medical research, in engineering and many more.

Representing Probabilities

A probability is represented by a number between 0 and 1. An event that is certain to happen is assigned by the probability of 1 If not certain to happen is assigned by the probability of 0.

Lets give an example of a simple event. When you toss a coin, You have ½ probability of getting either heads or tails, because for a fair coin they have the same chance of occuring.

Combining Probabilities

Lets say we roll two dice. Our purpose is to get at least one 6 from the twodice. Since a dice is six sided, the probability of getting 6 is 1/6 for one dice. Since we have two dice, we have to add both dice’s probabilities.

1/6 + 1/6 = 1/3As a result, the probability of getting a six from two dice is 1/3.

Now suppose we have five coins and this time we want to get heads for all of them. The probability of getting a head for a dice is ½. If we toss all of them in the air and want them to be heads, the formula will be: ½ × ½ × ½ × ½ × ½ = 1/32 We use multiplication here, because we want all the coins to be heads.

What is MEAN, MEDIAN & MODE in Statistics?

What is MEAN?

Statisticians call it mean, but another word for mean can be average. The mean of a set of N numbers is the sum of the numbers, divided by N.For example, in the data set {2, 5, 5, 8, 10} => (2 + 5 + 5 + 8 + 10) / 5 = 6

What is MEDIAN?

Median is the middle number of a set. For example, in the data set {2, 5, 5, 8, 10, 12} => (5 + 8) 2 = 6.5. In this situation median is the mean of two numbers, because there are even number of numbers in the data set.

What is MODE?

Mode is the most common value in the set. For example, in the data set {2, 5, 5, 8, 10, 12} => The mode is 5, because 5 appears the most in the set.

Citation

http://philosophy.hku.hk/think/stat/

Further ReadingsLarry Gonick and Woollcott Smith (1993), The Cartoon Guide to Statistics. New York: HarperCollins. A detailed and amusing guide to doing statistics.D. Huff (1973), How to Lie with Statistics. Harmondsworth, Middlesex: Penguin. A classic guide to misleading uses of statistics.A. J. Jaffe and Herbert F. Spirer (1987), Misused Statistics: Straight Talk for Twisted Numbers. New York: Marcel Dekker. A more up-to-date work on abuses of statistics.J. D. McGervey (1986), Probabilities in Everyday Life. Chicago: Nelson-Hall. A guide to gambling of all kinds, whether at the casino, on the horses or on the stock market.Judith M. Tanur et al., eds. (1989), Statistics: A Guide to the Unknown. Pacific Grove, CA: Wadsworth. Lots of real-world examples of applying statistical techniques in the biological, social and physical sciences.David Salsburg (2001) The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century W H Freeman & Co. A lot of case studies and information about famous statisticians.StatSoft, Inc. (2002). Electronic Statistics Textbook. Tulsa, OK: StatSoft. WEB: http://www.statsoft.com/textbook/stathome.html. An online reference for some of the more techinical concepts in statistics.