The most important reason that you want to look at quartiles is to see if there is any evidence of a linear trend in your data. If you have a series of numbers, say for example, and you take a quarter, you will find that it gives you a straight line graph. This means that the values of the variable are all on the same line and there is no indication that they are moving either up or down.
The second reason that you might want to consider using quartiles is when you are analyzing data with a log normal distribution. The log-normal distribution is a mathematical model that indicates that the value of one random variable can be predicted by the value of another random variable. For example, in the above example, if you know that the mean value of each of the data points falls between zero and four, you can predict that the mean value of each of the numbers within the data range falls between zero and one. You can use this information to conclude that the average value of each of the data points is between one and three.
Quartiles can also be useful if you are looking at samples that are not normally distributed. If you have a series of numbers that are all between three and nine, and then divide them into quartiles, you will see that there are four data points that fall in between three and nine, five data points that fall between ten and nineteen, and five data points that fall between twenty and thirty. By taking a quarter of these points, you will get a line that shows a steady upward slope, which suggests that the range of values in the data range is increasing over time.
Finally, if you have a series of observations with values that are above or below the mean, but there is not a linear trend, you can make use of quartiles. The difference between the highest and lowest values is called the variance. When you take a quarter of all the data points and divide them in half, you will find that there is a difference of about two standard deviations between them. This indicates that there is about a twenty percent difference in the average value between the highest and lowest data point.
By using these methods, you can figure out whether or not there is a linear trend, which means that if you have a series of observations and dividing them into quartiles, you will be able to identify the average value of each data point in the series. The size of the quartic indicates what the range of values is.
If you find that there is no evidence of a trend, then it is safe to conclude that there are more than enough data points in the series to show the same average value for the data. If however, there is a linear trend, then there may be too many data points to use a quarter and there may not be enough data points to go from one quarter to another.
In summary, there are many uses for quartiles. If you are looking for a way to determine whether or not there is a trend in your data, it is wise to use quartiles, especially if it is an exponential distribution. You can also use quartiles to help determine whether or not there is too much variation in the data, such as if the data is being collected from a log normal distribution. As you can see, using quartiles in statistics has many uses and they are very useful.
