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Did you ever think about Parameter vs statistic? Most people similarly use these two terms. But are they the same? Let’s find it out in this academic blog. Parameters are numbers used to define the entire population. But, statistics describe the property of a sample. One example of a population parameter is the average height of people in the United States. Again, the average income of a U.S. sample is a sample statistic. You can get the mean income by both values. But one is a parameter, and the other is a statistic. Here we will find out sample statistics.

A Definition of a Parameter and a Statistic

A parameter is a fixed measure that describes an entire population. A group of all the units being looked at that have some things in common. Also, it is based on all the parts of that population. On the other hand, a statistic is a sample property. It is how you define statistic vs parameter.

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The parameters and Statistics – Entire population types

Population parameters and statistics both talk about groups. Also, the Parameters and sample statistics are both ways to talk about groups.

Numbers are used to sum up the sample proportion or a population in parameters and statistics. You can judge a lot of different things, which leads to many kinds of parameters as well as statistics. For instance, are you measuring a part’s length (continuous) or whether or not it passes an inspection (categorical)?

When you use a continuous scale to measure a property, you can figure out different summary values for statistics and parameters. It includes means, medians, and standard deviations. Also, you come across correlations.

When the trait is a category, the parameter statistics is usually a proportion, like the number of people who agree with a specific law.

Top 3 common Population parameters

Both the parameters and the statistics use numbers to determine the population’s properties. But, there is a possible range that you get to evaluate. The population parameters play a vital role in the sample statistics. As a result, you get a variety of parameters and statistics. 

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You can find three common types of parameters. Following are the types with symbols:

1. Range

The histogram of A and C shown here refers to diagram explanation of range.

In a few words, we can say the following: Range = Maximum Value–Minimum Value. For example, in the data set 4,6,10,15,18, the highest number is 18, and the lowest is 4. The range is 18-4 = 14.

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2. standard deviation (σ)

The image shows standard deviation.

SD is an abbreviation for “standard deviation,”. It is usually written in lowercase. The Greek letter (sigma) is used for the population standard deviation. Also, the Latin letter ‘s’ works for the sample standard deviation. It is both for mathematics and statistics.

3. Variance (σ2)

The variance formula is shown in the image.
  1. The term “variance” refers to a statistical way to measure how far apart the numbers in a set are from each other. More specifically, variance indicates the distance in a set seems to be from the mean (average) and, by extension, from every additional amount in the collection. This symbol, σ2, is often used to show variation.
    With these, you will be able to estimate population parameters. On the other hand, one should depend on a representative sample to get the statistical inference. Also, the parameter vs sample statistic goes hand in hand.

How do you find population parameter and statistics?

When values are given to the parameters, like slope = 2 and y-intercept = 3, and substitution is done, the arising equation, y = 2x + 3, is for a precise straight line and is no longer parametric. The “parameter” in the system of equations x = 2t + 1 and y = t2 + 2 is t.

The “statistics” part of data science includes many ways to find actual statistics, which are numbers you can use to generalize a population.

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Parameter vs statistic examples

In every fact of mathematics or statistics, it is essential to have a good example. Let’s list some models on a random sample that sets a standard. The following criteria will describe how the sample data and summary value can be statistics or parameters. The sample statistic vs population parameter example is stated below.

Examples of Parameter

  1. Mean weight of all American women
  2. The median income of a nation
  3. The proportion of the entire group preferring fruit juice over tea
  4. The standard deviation of transaction times in Yes Bank

Examples of Statistics

  1. Mean weight of the 100 American women
  2. Median income randomly 50 samples of individual income
  3. The standard deviation of numerical value 500 of banking transaction
  4. The latest health care proposal of 200 people.

With the above examples it is quite easy to find out true population parameter of the whole population. On the other hand the descriptive statistics of simple random sample range.  However, to have more clarity, you may visit the below mentioned video.

Choosing between a parameter and sample statistics

How do you know if a summary value is a parameter or a statistic when listening to the news, reading a report, or taking a statistics test?

Sampling methods are almost always used in real-world studies because populations are usually too big to measure. Remember that you need to be able to measure the whole population to find the exact value of a parameter. You can collect data on college students or some other populations.

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On the other hand, researchers choose the populations for their studies and can choose a very narrow one. A researcher, for statistic vs parameter example, could define the population as a specific neighborhood, the 100 U.S. Senators, or a particular sports team. There’s no reason why you couldn’t talk to everyone in those groups! It is a random sampling method for an unbiased estimate. 

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The trick is to determine if the summary value is for the whole population or just a tiny part. Carefully read the story and decide for yourself. Think about the following:

When a description says that a sample was used, the overall value is a statistic.

If there are many people or it would be hard to measure them all, the total value is a statistic.

But if the researchers define the population as a small group that is not too hard to reach, they might be able to measure the whole group. The value of the summary could be a parameter.

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What is inferential statistics?

The image shows what is inferential statistics with the help of image.

Statistical inferences utilize measurements. It is usually from a sample of subjects in an experiment. It is meant to compare the treatment groups and make generalizations. It is all about the more significant population of subjects. Also, there are many different kinds of inferential statistics. Each one is for another type of research design and sample size. Also, you can get statistic vs parameter quiz questions. You can also use educated guesses of the standard parameters of the population. Also, one can get different samples to define the specific group.

Frequently Asked Questions

What is a parameter vs statistic?

The population mean is an example of a parameter. It can be hundreds of millions. A statistic, on the other hand, is a number that describes a sample (e.g., sample mean). It is meant for small populations. The goal of quantitative research is to find parameters that help us understand how populations are made up. It is how the difference between statistic and parameter has its place.

What is hypothesis testing?

Hypothesis testing is a type of statistical inference. It uses data from a sample. The purpose is to make conclusions about a parameter or probability. Also, it deals with the distribution of the given population.

Which is better ‘ statistic or parameter’?

A parameter is a lot like a statistic. These sentences describe groups, like “50% of dog owners like X Brand dog food.” A statistic is different from a parameter in that it represents a sample. A study shows an entire population.

What is the role of variable and parameter in statistics?

Variables are amounts that are different for each person. On the other hand, parameters have nothing to do with actual measurements or qualities. Instead, they are the numbers that make up a theoretical model.

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Ian Fleming