Statistics - Random Sampling - Central Limit Theorem

Random Sampling

is a sampling method of choosing representatives from the population wherein every sample has an equal chance of being selected.

Population

includes all of its elements from a set of data.

Sample

consists of one or more data drawn from the population. It is a subset, or an incomplete set taken from a population of objects or observations

Simple Random Sampling
Systematic Random Sampling
Stratified Random Sampling
Cluster Random Sampling

Four Types of Random Sampling

Simple Random Sampling

is the basic sampling technique where we select a group of subjects (a sample) for study from a larger group (a population).

Systematic Random Sampling

involves choosing your sample based on a regular interval, rather than a fully random selection. It can also be used when you don't have a complete list of the population.

Stratified Random Sampling

s used when you want to ensure that specific characteristics are proportionally represented in the sample. You split your population into strata (for example, divided by gender or race), and then randomly select from each of these subgroups.

Cluster Random Sampling

is used when you are unable to sample from the entire population. You divide the sample into clusters that approximately reflect the whole population, and then choose your sample from a random selection of these clusters.

Parameter

a measure that is used to describe the population while statistic is a measure that is used to describe the sample

Mean

is the sum of the data divided by the number of data.

Statistic or Sample Statistic

is any quantity computed from values in a sample which is considered for a statistical purpose

Sample Mean

is the average of all the data of the samples

Sample Variance

is the computed variance of the elements of the sample. s^2 is used to represent sample variance

Sample Standard Deviation

s the computed standard deviation of the elements of the sample. 𝒔 is used to represent sample standard deviation

Sampling Distribution of the Sample

is a frequency distribution using the computed sample mean from all the possible random samples of a particular sample size taken from the given population.

Mean of the sampling distribution of the mean

is the mean of the population from which the scores were sampled.

Variance of the sampling distribution of the mean

is the population variance divided by N, the sample size (the number of scores used to compute a mean). Thus, the larger the sample size, the smaller the variance of the sampling distribution of the mean

Standard error of the mean

is the standard deviation of the sampling distribution of the mean

Finite Population

is one that consists of a finite or fixed number of elements, measurements, observations

Infinite Population

contains, hypothetically at least, infinitely elements.

Standard error of the mean

The standard deviation (𝜎𝑥̅ ) of the sampling distribution of the sample means is also known as?

The standard deviation (𝜎𝑥̅ ) of the sampling distribution of the sample mean

It measures the degree of accuracy of the sample mean (𝜇𝑥̅ ) as an estimate of the population mean (𝜇).

The definition of the sampling distribution of the sample mean for the normal population when the variance is known or unknown

is used to determine the probability value of a certain event for small and large samples. This serves as a tool for statisticians or any interesting group who wants to test the sample mean using statistical formulas and to make a rightful decision in the future.

Central Limit Theorem

is a fundamental importance in statistics because it justifies the use of normal curve method for a wide range of problems.