The average rate of changes is the average value obtained by taking a random difference, or a mean, of two independent variables over a specified period of time. The average rate at which a
random change occurs is called the random variable. A single parameter, the rate at which a random variable will change, can be used to describe the behavior of any system. A common example of a parameter is the slope of the average curve, which represents the amount of change in the mean value over the interval of time over which the interval occurs. An example of a statistic is the rate at which an average number of whiteheads develops into blackheads.
Average rate of changes can also be defined as the average change from one set of random variables over a specified interval of time to another. For instance, the rate at which a person
grows taller varies from person to person and day to day. A person can grow as much as seven inches within one month, while it takes about twenty years for most people to grow at least one
inch each year.
Some examples of statistics involving random variables include a random event such as the birth of the first baby, a crime or arrest, the death of someone close, the creation of a new
product, the sale of a product, or the loss of life. Other examples of statistics are the birth rate among new immigrants, the increase in sales at a company in a given year, the rise in the price
of commodities over a specific period of time, or the occurrence of a disease outbreak. There are other examples of statistics that involve random variables such as the number of ticks falling
on an animal skin and the amount of energy expended to move one centimeter in one second. When using the average rate of change to characterize a certain phenomenon, it is important to
note the effect of the speed at which changes occur, or the magnitude of changes. While the rate at which a random variable change is important, it is also important to consider what the
impact would be if the rate was significantly different from what is expected. Some examples of the difference between what is expected and what is observed are: the difference between a
person growing one inch each year and the person growing an inch every six months. and the difference between someone reaching a peak height of ten feet in one second and the person
reaching ten feet in fifty-four milliseconds.
Some examples of statistics with random variables include the changes that occur with random distribution of individuals within a population, the change in the average height of a certain
population over time, and the change in the population size of a town over a period of time. Another example is the change in the population size of a town that has undergone a flood. a
flood may cause the removal of people from a certain area, resulting in an increased percentage of the original population of that town. This example demonstrates the effect of time and distance on the average rates at which changes occur and how they affect a certain quantity of the random variable.
It is important to understand the effects of time and distance on the average rate at which changes occur. For instance, if you measure a population over a period of time, you can look for
an effect of the number of people being removed in the number of those being displaced over the length of the time in which you measured. If the displaced individuals are more likely to
return after the displacement than they were to leave, then the displacement is more likely to be caused by the amount of time you have taken to measure.
There are other examples of statistics involving the average rate at which changes occur that are similar to those listed above and, therefore, provide an insight into the effects of time and
distance. These include the effect of time on the average frequency of births, the rate at which people move, and the effect of distance on the average travel distance of individuals.