# How to Understand Random Sampling and Variation in Samples?

## Step by step guide to Understanding Random Sampling and Variation in Samples

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen.

In this case, a randomly selected sample is an unbiased representation of the total population.

In this method, the required people or objects are randomly selected from the list of the population that has been numbered and prepared for this purpose. According to the law of probability, selected items must have the same features as the population from which they were selected.

Random sampling is used when the volume of the sample group is large. This sample is selected based on the principle that all members of the study population are similar and homogeneous; Therefore, the researcher can select them after determining the number and volume of the sample.

Representative sample: a sample that is similar to the entire population. This sample accurately reflects the characteristics of the larger group.

Systematic sample: a sample chosen according to a rule or formula (Example: survey every 10th person through the door). In this case, the selection of samples is done in such a way that according to the random starting point, but with a fixed and periodic interval. This interval is called a sampling interval and is obtained by dividing the population size by the desired sample size.

Convenience sample: a sample that is easiest to reach (Example: survey the first 10 people through the door). This is the most common sampling method because it is a fast, uncomplicated, and cost-effective way. Other reasons for the popularity of this method include easy access to members to be a part of the sample.

Voluntary-response sample: members volunteer to be in the sample. In this case, participants usually respond to surveys voluntarily and share their opinions on topics of interest.

## Understanding Random Sampling and Variation in Samples Example 1:

Choose a sample of size $$8$$ from $$56$$, using systematic random sampling.

Solution:

Determine $$K$$, $$K=\frac{56}{8}=7$$, this means that you have to include every 7th member of the population after choosing a random start.

Suppose you picked 5.

Getting 8 members you will have: $$5, 12, 19, 26, 33, 40, 47, 54$$

## Understanding Random Sampling and Variation in Samples Example 2:

Lisa put some marbles into a box. Then, he drew 5 marbles out of the box. Is this a random sample of the marbles in the box? Why or why not?

Solution:

in a random sample, every person or item has an equal chance of being chosen. Since every marble had an equal chance of being picked, in this case, it is a random sample.

## Exercises for Understanding Random Sampling and Variation in Samples

### For each situation below, determine what type of sampling technique is used (simple Random Sampling, Systematic Sampling, Convenience Sampling, or Representative Sampling).

1. A researcher wants to sample ten houses from a street of 110 houses.   Every 12th house is beginning with house #10. The houses selected are 10, 22, 34, 46, 58, 70, 82, 94, and 106.
2. A researcher wants to select eight students for a survey. Each student’s name is placed in a hat and 8 names are selected.
3. The researcher stands at a shopping mall and selects the first 55 shoppers as they walk by to fill out a survey.
1. Systematic Sampling
2. Simple Random Sampling
3. Convenience Sampling

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