- Simple Random Sampling and Sampling Distribution
- Sampling Error
- Stratified Random Sampling
- Time Series and Cross Sectional Data
- Central Limit Theorem
- Standard Error of the Sample Mean
- Parameter Estimation
- Point Estimates
- Confidence Interval Estimates
- Confidence Interval for a Population mean, with a known Population Variance
- Confidence Interval for a Population mean, with an Unknown Population Variance
- Confidence Interval for a Population Mean, when the Distribution is Non-normal
- Student’s t Distribution
- How to Read Student’s t Table
- Biases in Sampling

# Simple Random Sampling and Sampling Distribution

### Simple Random Sampling

Simple random sampling is a type of sampling method, in which each element of the population has an equal chance of being selected in the sample.

A simple random sample can be selected as follows: List all the items in the population say from 1 to N, where N is the total number of items in the population. We have given an identification number (1 to N) to each item in the population. Using a random number algorithm (a computer based random number generator or some other method of generating random numbers) select n units from the list of N units one at a time without replacing the items.

This method of sampling is useful where the population is small. A problem with this method is that the sample may not be a good representative of the population as it may not evenly capture all dimensions of the population.

**Sampling Distribution**

A sampling distribution is a probability distribution of the sample statistic. An example of a sample statistic is the **mean** of sample data.

A sampling distribution of the mean is the probability distribution of sample mean obtained by drawing all possible samples of the same size from the same population.

Let’s say we are looking at a population of 500 stocks. We can draw random samples of 50 stocks from the population and calculate their mean returns. The ‘**sample mean returns**’ is a sample statistic. We can draw many such samples of 50 stocks and calculate sample mean returns for each random sample. All the sample mean returns are an estimate of the population mean. These ‘sample mean returns’ can be plotted as a sampling distribution of the mean.

Since the process is based on random sampling, the sampling distribution will resemble a normal distribution, even if the population is not normally distributed.

Just like any other distribution, a sampling distribution can be described by its mean and standard deviation.

**Mean (****μ):** The mean of the sampling distribution equals the mean of the population.

**Standard Deviation (****σ):** This measures how spread out the distribution is and represents approximately the amount by which the sample means deviate from the population mean. Note that the larger the sample size, the smaller will be the standard deviation. The standard deviation of the sampling distribution is called the **standard error**.

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