Key Concepts in Statistics
This lesson describes the key concepts in statistics.
Key Concepts
Population vs. sample
The population is a collection of all the observations related to the problem at hand. It is not practical to gather knowledge about all the observations. So, we choose a good amount of observations, from the population, which represent our sample.
Statistical Inference
The process of estimating a population parameter from a sample statistic is called statistical inference. It has two major areas estimation and statistical hypothesis testing.
Parameter vs. statistic
Values like mean and standard deviation for the population are called parameters while the samples are called statistics. We can estimate the parameter value using the statistic value. The gap between the sample statistic and population parameter is called the sampling error.
Central Limit Theorem
The Central Limit Theorem states that if you have a large population with mean $\mu$ and standard deviation $\sigma$ and it takes sufficiently large random samples from the population with replacement (samples drawn are independent), then the distribution of the sample means will be approximately normally distributed.
Sampling Distribution
The probability distribution of a statistic is called a sampling distribution. It depends on the distribution of the population, the size of the samples, and the method of choosing the samples. The standard deviation of the sampling distribution is called the standard error. The standard error of the sampling distribution decreases as the sample size increases.
Constructing the sampling distribution

Take a sample size “$n$” and a sample statistic say mean “$\bar{x}$”.

Randomly choose the sample values according to the sample size.

Calculate the chosen sample statistic $\bar{x}$ on the given sample and store it.

Repeat from the second step up to a multiple numbers of times.
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