One advantage of inferential statistics is that large predictions can be made from small data sets. However, if the sample is not representative of the population then the predictions will be incorrect.
When performing an experiment or gathering data for statistics, it would be very difficult to gather information for every member of the group's population. Instead, one can gather information from a sample large enough to be representative of the population.
The law of large numbers is a principle of probability and statistics. It states that as a sample size increases, its mean will get closer to the average of the whole population.
This question gets at the core of statistics. Statistics has two central ideas: a population, and a sample. All of statistics is an attempt of ways to understand the entire population without actually observing every entity within it - by choosing and observing only a sample (a sub-set) of the full population. As an example, if we wish to find the average ratio of males to females on the entire planet, we can do this one of two ways. Either we actually count every person on the planet and after a very lengthy process we will have the answer. Or alternatively, we can use statistics to simplify the effort by selecting a smaller group of people (we call this a sample) that we believe will accurately represent, without any bias, the entire planet's population. If we take this second approach, also called a sampling approach, one of the most important decision to take is the number of people to include in this group (in the sample). This number - known as the "Sample Size" - is the number of a population that will be evaluated as representing the entire population, and from which statistics will be derived. Choosing a sample size too large will require extra unnecessary effort, but one too small will not accurately represent the entire population (and the statistics or averages derived might not be correct - we won't even know IF the statistics are correct or incorrect - so we won't know if we need to repeat with another sample).
A sample consists of a small portion of data when a population is taken from a large amount.
The population is the set of all things which you wish to study. However, because collecting information from a large, possibly infinite, population is likely to be prohibitively large and time consuming, it is collected from only some members of the population. This subset is a sample.The population may, but need not, consist of people. It could be the set of cars, or plots of land. There are a number of different ways of selecting samples: how the sample is selected will influence the quality of the statistics collected and, therefore, the validity of any conclusions.
The sample must be large and random.
that you have a large variance in the population and/or your sample size is too small
It can get a bit confusing! The estimate is the value obtained from a sample. The estimator, as used in statistics, is the method used. There's one more, the estimand, which is the population parameter. If we have an unbiased estimator, then after sampling many times, or with a large sample, we should have an estimate which is close to the estimand. I will give you an example. I have a sample of 5 numbers and I take the average. The estimator is taking the average of the sample. It is the estimator of the mean of the population. The average = 4 (for example), this is my estmate.
Because a sample is information obtained from the population that will be used in hypothesis testing. WER 1.19.2011 Samples are used to save time and money when the population is large and when the units must be destroyed to gain information.
A large trial is necessary to provide good sample that is representative of the population
Because the whole population might be too large to sample. A good example is the population of the world. At nearly 7 billion people, it would be unrealistic to sample each person to determine some factor that you are looking at. Generally, we sample a subset of the population, taking into account differences (or errors) that might result, in this case, regional and cultural, in order to estimate the behavior of the larger population.
In response to your question. I can not give you a single "mathematical concept." An important concept in the descriptive statistics that you mention is that they should provide some understanding to a population which I can not completely know or measure. Therefore I must sample the population and describe it with statistics such as the mean. I will list some necessary conditions for statistics to be representative of a population. In statistical analysis, given any set of numbers, it is possible to calculate numerous statistics such as the median, mean, mode and range. Another common statistic is the standard deviation. In making inferences to the population, the sample size should be adequate, the sample shoud be taken in an unbiased manner, and the sample should be taken from the same population. The population should be stationary in time. It's distribution should not be changing with time. This may be difficult to understand, but I'll give you an example: Let us suppose that we are studying brake failures on cars, so we survey all brake failures from 1950 to 2004, a very long period so we have a large sample. But brakes in 1950 were different than in 2004, because brake failures motivate car companies to improve their design. Our statistics will not be representative of new cars being purchased.
Yes, but that begs the question: how large should the sample size be?
A sample! And the large group is called the population.
Assuming that the population was carefully defined, the sample population was carefully and correctly chosen, and that there were significant results, then the implication is that the results of the study, within the confidence limits indicated, hold true for the population at large.
If I take 10 items (a small sample) from a population and calculate the standard deviation, then I take 100 items (larger sample), and calculate the standard deviation, how will my statistics change? The smaller sample could have a higher, lower or about equal the standard deviation of the larger sample. It's also possible that the smaller sample could be, by chance, closer to the standard deviation of the population. However, A properly taken larger sample will, in general, be a more reliable estimate of the standard deviation of the population than a smaller one. There are mathematical equations to show this, that in the long run, larger samples provide better estimates. This is generally but not always true. If your population is changing as you are collecting data, then a very large sample may not be representative as it takes time to collect.
Span the full spectrum of a population's genetic variation. <apex> Reflects the genetic variation of a population...
A sample of size 100.
Vermont does not have a large Hispanic population. The 2010 census statistics reflect that there were approximately 5500 individuals who were Hispanic or Latino.
A large sample will reduce the effects of random variations.