what are the benefits to having a class representative?

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In statistics, we're often interested in studying characteristics of specific populations. For example, we might be interested in studying:

• The overall chore satisfaction of mechanical engineers in a certain city.
• Political preferences of individuals in a certain county.
• The age distribution of individuals in a certain country.
• Movie preferences of students in a certain school.

In each of these examples, nosotros want to gain an understanding of a certain population.

Population:The entire group of individuals you are interested in studying.

Unfortunately, it can be expensive and time-consuming to get together data for every individual in a population, which is why researchers typically gather data for asamplefrom a population and and then generalize the findings from the sample to the larger population.

Sample:A subset of the population.

For example, suppose we want to understand the film preferences of students in a certain school that has 1,000 total students. Since it would take likewise long to survey every private educatee, we might instead take a random sample of 100 students and ask them well-nigh their preferences.

The one,000 students represent the population, while the 100 randomly selected students correspond the sample. Once nosotros collect information for the sample of 100 students, we tin can and then generalize those findings to the overall population of one,000 students,simply only if our sample is representative of our population.

Representative sample: A sample in which the characteristics of the individuals closely lucifer the characteristics of the overall population.

Ideally, nosotros want our sample to be like a "mini version" of our population. So, if the overall educatee population is equanimous of l% girls and fifty% boys, our sample would not be representative if it included 90% boys and only 10% girls.

Or, if the overall population is composed of equal parts freshman, sophomores, juniors, and seniors, and so our sample would non exist representative if information technology only included freshman.

The Importance of Obtaining a Representative Sample

The reason we want a representative sample is and so that we can confidently generalize the findings from the sample to the population.

For example, suppose nosotros want to know what percent of students at a certain school adopt "drama" as their favorite movie genre. If the full student population is a mix of 50% boys and fifty% girls, then a sample with a mix of xc% boys and ten% girls might pb to biased results if far fewer boys adopt drama as their favorite genre.

Or, if the full population is a mix of equal parts freshman, sophomores, juniors, and seniors, and so a sample with only freshman might lead to biased results equally well if younger students (e.g. freshman) tend to prefer drama at much higher rates than older students.

If the characteristics of individuals in our sample practise non closely match the characteristics of the individuals in the overall population, then we cannot generalize the findings from the sample to the overall population with any confidence.

How to Obtain a Representative Sample

To maximize the chances that we obtain a representative sample, we need to focus on two things when obtaining our sample:

one. Use an appropriate sampling method.

There are many means to obtain a sample from a population, simply here are three methods that are likely to obtain a representative sample:

Simple random sample:Randomly select individuals through the apply of a random number generator or some means of random selection.

• Case: Assign a number to all 1,000 students. And then, employ a random number generator to select 100 random numbers and use the corresponding students as members in the sample.
• Benefit:Simple random samples are commonly representative of the population we're interested in since every fellow member has an equal chance of existence included in the sample.

Systematic random sample:Put every member of a population into some order. Choose a random starting signal and select every n^th member to be in the sample.

• Case: Create a list in alphabetical lodge based on the last name of all 1,000 students, randomly choose a starting betoken, and selection every tenth student to exist in the sample.
• Benefit:Systematic random samples are ordinarily representative of the population we're interested in since every member has an equal adventure of beingness included in the sample.

Stratified random sample: Divide a population into groups. Randomly select some members from each group to exist in the sample.

• Case: Carve up upwards all students according to their grade – freshman, sophomores, juniors, and seniors. Randomly select 25 students from each grade to be in the sample.
• Benefit:Stratified random samples ensure that an equal number of students from each form are included in the sample.

two. Make sure the sample is large plenty.

Along with using an appropriate sampling method, it'due south important to ensure that the sample is big enough so that nosotros accept enough data to generalize to the larger population.

For example, a sample of eight students – a boy and a girl from each course – might represent a mini version of the larger population, but information technology's probably not large enough to capture all of the variability that naturally exists in the responses of the students.

Then, how big does your sample need to exist?

That depends on the following factors:

• Population size: In general, the larger the population size, the larger the sample needs to be. For example, you lot'll need a much larger sample if yous desire to generalize your findings to an entire country compared to a single city.
• Confidence level: How confident yous desire to be that the true population value you lot're interested in falls within your confidence interval. Common confidence levels include ninety%, 95%, and 99%. The higher the confidence level, the larger your sample needs to be.
• Margin of fault: How much fault you lot're willing to tolerate. No sample will exist perfect, then you must be willing to have at least some amount of fault. Near research studies volition report their findings with a margin of error, for instance "40% of students reported thatdramawas their favorite picture show genre, with a margin of mistake of +/- 5%." The lower the margin of error, the smaller your sample needs to be.

There are plenty of sample size calculators online to aid you lot make up one's mind how big your sample needs to be based on these factors. This computer from Survey Monkey is peculiarly piece of cake to use.

Things to Keep in Mind

Fifty-fifty if you use an appropriate sampling method and ensure that your sample is large enough, keep in mind the following things:

• There volition always besomesampling error. The sample volition never be perfectly representative of the larger population.
• In full general, the larger the sample, the more likely information technology volition be representative of the population.
• You lot demand to strike a balance betwixt sample size and real-earth variables like fourth dimension and cost. A larger sample might accept a college chance of representing the overall population, but it might exist more expensive and time-consuming to obtain.

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Source: https://www.statology.org/representative-sample/

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