Relationship Between Sample and Population
Sample is a subset of population. Basically we make use of statistical values to estimate parameters. There are different techniques. Let us go through each of them:
Sampling
Sampling is a fundamental concept in which we select random samples from the population. We use those sample to draw statistical inference about the population. It is to be noted that Random Sampling should be used so that our samples are diverse in nature. If samples are not randomly selected, then it will generate biased results. Different Sampling Techniques include:
- Simple random sampling
- Systematic sampling
- Stratified sampling
- Cluster sampling
- Probabilistic Sampling
Law of Large Numbers
Law of Large Numbers is a mathematical theorem which states that as the sample size increases, the sample mean becomes closer to the population mean. For example: Suppose we have a huge dataset which comprises of 50 numbers. Now if we select two or three numbers as our samples, then the average will not be even close to the average of the number. However if consider sample size 20-20, then the sample mean will come closer to the population mean.
Central Limit Theorem
Before going through the central limit theorem, we must be familiar with Normal Distribution. Normal Distribution or Gaussian distribution is a bell shaped curve which maintains its symmetry about the mean.
This theorem states that as the sample size increases the sample means follow a normal distribution or the Gaussian Distribution.
Parameters and Statistics
Statistics and parameters are two fundamental concepts in statistical theory. Although they may sound equal, there is a sharp difference between the two. One is used to represent the population, and the other is used to represent the sample. Now we will focus on the sample and population:
Population: A population refers to the whole data. It is the dataset that the statisticians use to derive conclusions or gain insights about the data.
Sample: Sample refers to the small dataset. It is considered to be a subset of population. Since population can be huge and may be difficult to examine, Statisticians usually consider a subset or sample, perform Statistical analysis and derive conclusions about the Population.
It is to be noted that the sample to be selected should be random in nature. If the subgroup or sample is not randomly selected, it may produce biased results.
Table of Content
- Parameters
- Statistics
- Relationship Between Sample and Population
- How to derive Population Parameter using Statistics?
- Types of Parameters and Statistics
- Difference between Parameters and Statistics
- Solved Questions on Parameters and Statistics
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