Normal Distribution

Statistics encompasses anything where data can be taken. When graphing data, the graph can be catorgerized into different shapes. See below:

But what do these graphs mean and how do you get them? The y-axis in these graphs represents the data points. For example, if graphing different heights of trees, the y-axis would be heights. Each curve is only a rough representation of the data. There are actually rectangles making up the area of the curve, and the line is fitted ontop. These rectangles and their preciseness is dictated by their bin width. The most useful shape is normal distribution. There is an equal distribution of the area on each side of the curve. With a normal distribution, you can use something called standard deviation to further analyze data. Standard deviation is how percentages are found from a normal distribution chart easily and without calculous. The basic rules regarding standard deviation are located below.

The middle line, or 0, is the mean or more commonly known as the average. Each standard deviation from there on is then in terms of that mean. Using the example of heights, most people will be around the average height. There will generally be an equal number of people with heights above and below this average. This is reflected in the symmetry of the graph. There are of course outliers with people being extremely tall or short, but because of laws regarding errors, this will be random and does not greatly affect standard deviation.

Standard deviation varies with each data set. It is a measure of stretch for any given points. The smaller the deviation, the closer to the mean each data value is. Even if there is a standard deviation of 20 in one graph and a standard deviation of 10 in another, the percentage rules still hold true. This is why the 68-95-99.7 rule holds true regardless of the numerical value of deviation. This makes it easier to find areas without having to use calculus since this is a general rule.