What Is a Parameter? Its differences with statistics and some examples:

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Parameter definition and frequently asked questions with explainations

It is a measure of a characteristic of an entire population (a mass of all units under consideration that shares common characteristics) based on all the elements within that population. For example, people living in one city, all-male teenagers globally, all features in a shopping trolley, or all students in a classroom. 

What Is a Parameter?

If you ask all employees in a factory what kind of lunch they prefer and half of them say pasta, you get a parameter here – 50% of the employees like pasta for lunch. On the other hand, it’s impossible to count how many men in the whole world like pasta for lunch, since you can’t ask all of them about their choice. In that case, you’d probably survey just a representative sample (a portion) of them and extrapolate the answer to the entire population of men. It brings us to the other measure called a statistic.

It’s a measure of characteristic saying something about a fraction (a sample) of the population under study. A model in statistics is a part or portion of a community. Here we see what is the parameter of interest and its related topics in detail. The goal is to estimate a specific population parameter. You can draw multiple samples from a given population, and the statistic (the result) acquired from different models will vary, depending on the pieces. So, using data about a sample or portion allows you to estimate an entire population’s characteristics. 

Parameter vs Statistics 

Can you tell the difference between statistics and parameters now?

A parameter is a fixed measure describing the whole population (population being a group of people, things, animals, phenomena that share common characteristics.) A statistic is a characteristic of a sample, a portion of the target population. 

A parameter is a fixed, unknown numerical value, while the statistic is a known number and a variable which depends on the portion of the population.

Sample statistic and population.

Parameters have different statistical notations: 

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In population parameter, the population proportions represented by P, mean is represented by µ (Greek letter mu), σ2 represents variance, N represents population size, σ (Greek letter sigma) represents standard deviation, σx̄ represents Standard error of the mean, σ/µ represents Coefficient of variation, (X-µ)/σ represents standardized variate (z), and σp represents standard error of proportion. 

In sample statistics, mean is represented by x̄ (x-bar), sample proportions represented by p̂ (phat), s represents standard deviation, s2 represents variance, the sample sizes represented by n, sx̄ represents Standard error of the mean, sp represents standard error of a proportion, s/(x̄) represents Coefficient of variation, and (x-x̄)/s represents standardized variate (z).

Examples of Parameters:

20% of U.S. senators voted for a specific measure. Since there are only 100 senators, you can count what each of them voted.

Examples of Statistic:

50% of people living in the U.S. agree with the latest health care proposal. Researchers can’t ask hundreds of millions of people if they decide, so they take samples or part of the population and calculate the rest.

What Are The Differences Between Population Parameters and Sample Statistics?

The average weight of adult men in the U.S. is a parameter with an exact value – but we don’t know it. Standard deviation and population mean are two common parameters. 

A statistic is a characteristic of a group of population or sample. You get sample statistics when you collect a model and calculate the standard deviation and the mean. You can use sample statistics to make certain conclusions about an entire population, thanks to inferential statistics. But, it would help if you had particular sampling techniques to draw valid conclusions. Using these techniques ensures that samples deliver unbiased estimates – correct on average. When it comes to based assessments, they are systematically too low or too high, so you don’t need them. 

To estimate population parameters in inferential statistics, you use sample statistics. For instance, if you collect a random sample of female teenagers in the U.S. and measure their weights, you can calculate the model mean. You can use the model mean as an unbiased estimate of the population mean.

Conclusion:

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Parameter vs statistic – both are similar yet different measures. The first one describes the whole population, while the second describes a part of the community.

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