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How do inferential statistics describe data differently than descriptive statistics?
The term "descriptive statistics" generally refers to such information as the mean (average), median (midpoint), mode (most frequently occurring value), standard deviation, highest value, lowest value, range, and etc. of a given data set. It is a loosely used term, and not always meant to contrast with inferential statistics as the question implies. But in the context of the question, descriptive statistics would be information that pertains only to the data that has actually been collected. In the case of an instructor calculating an average grade for a class, for example, the collected data would most likely be the only point of interest. Thus, descriptive statistics would be enough. However, it is more common for a researcher to use a sample of collected data to make inferences and draw conclusions about a larger group (or "population") that the sample represents. For example, if you wanted to know the average age of users of this site, it would be unrealistic to question every singe user. So you might question a small sample and then extend that information to all users. But if you found the average age in your sample to be 40, you could not immediately assume that 40 is the average for all users. You would need to use inferential statistics to calculate an estimate of how accurately your data represents the larger group. The most common way to do this is to calculate a standard error, which will produce a range within which the population average most likely (but not definitively) lies. Therefore, in the simplest description (inferential statistics are also a part of much more powerful tests outside of this answer), descriptive statistics refer only to a sample while inferential statistics refer to the larger population from which the sample was drawn.
Does descriptive statistics means parametric statistics?
No. Descriptive statistics are those that characterise samples without attempting to draw conclusions. The purpose of them is to help investigators to form an understanding of what the data might be capable of telling them. Descriptive statistics include graphs as well as measures of location, scale, correlation, and so on. Parametric statistics are those that are based on probabilistic models (ie, mathematical models involving probability) that involve parameters. For instance, an investigator might assume that her results have come from a population that is normally distributed with a certain mean and standard deviation; this would be a parametric model. She could estimate this pair of parameters, the mean and standard deviation, using parametric statistics, or test hypotheses about them, again using parametric statistics. In either case the parametric statistics she uses would be based on the parametric mathematical model she has chosen for her data.
How can statistics be applied in payroll?
Statistics are applied to payroll in many different ways. The determination of the unemployment rate is found by applying payroll statistics. Without applying statistics to payroll the unemployment rate would not be found.
What are the uses of statistics?
Statistics is primarily used either to make predictions based on the data available or to make conclusions about a population of interest when only sample data is available. In both cases statistics tries to make sense of the uncertainty in the available data. When making predictions statisticians determine if the difference in the data points are due to chance or if there is a systematic relationship. The more the systematic relationship that is observed the better the prediction a statistician can make. The more random error that is observed the more uncertain the prediction. Statisticians can provide a measure of the uncertainty to the prediction. When making inference about a population, the statistician is trying to estimate how good a summary statistic of a sample really is at estimating a population statistic. For example, a statistician may be asked to estimate the proportion of women who smoke in the US. This is a population statistic. The only data however may be a random sample of 1000 women. By estimating the proportion of women who smoke in the random sample of 1000, a statistician can determine how likely the sample proportion is close to the population proportion. A statistician would report the sample proportion and an interval around that sample proportion. The interval would indicate with 95% or 99% certainty that the population proportion is within that interval, assuming the sample is really random. School Grades, medical fields when determining whether something works, and marketing works
What is the difference between a probability distribution and sampling distribution?
A sampling distribution function is a probability distribution function. Wikipedia gives this definition: In statistics, a sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample). I would add that the sampling distribution is the theoretical pdf that would ultimately result under infinite repeated sampling. A sample is a limited set of values drawn from a population. Suppose I take 5 numbers from a population whose values are described by a pdf, and calculate their average (mean value). Now if I did this many times (let's say a million times, close enough to infinity) , I would have a relative frequency plot of the mean value which will be very close to the theoretical sampling pdf.
