# Parameter vs. Statistic: When to Use Statistic vs. Parameter (with Useful Examples)

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In the realm of statistics, it’s fundamental to distinguish between parameter vs. statistic, as both play instrumental roles in the study of data but represent different aspects of that data. Both these words give us information about a group, for example, a percentage of people who like dogs. But what is the difference between the two terms?

## Parameter vs. Statistic: The Main Differences

### Key Takeaways

• Parameters describe entire populations while statistics describe samples.
• Statisticians estimate parameters using statistics derived from sample data.
• Understanding the difference is essential for accurate statistical inference.

### Parameter vs. Statistic: the Definition

#### Defining Parameters

parameter is a numerical value that characterizes an entire population. It is a fixed number, although in practice it is often unknown and therefore estimated.

• Descriptive of a population
• Generally fixed but often unknown
• Not directly obtainable due to the impracticality of a complete population analysis

#### Defining Statistic

Statistics, on the other hand, are values that describe a sample, which is a subset of the population. These numbers are variable, as they can change with different samples even from the same population.

• Descriptive of a sample
• Variable and known
• Easier to obtain and used for making inferences about the population parameter

### When to Use Parameter vs. Statistic

Let’s say that a survey found that 70% of 500 school students have pets. For this survey, each and every one of these 500 students has been asked, so we know the answers from everyone in the entire population. Therefore, in this case, we have a parameter.

But what if you read an article that says that (all numbers assumed) 80% of Europeans have at least one car? It’s impossible to ask all the Europeans. Most probably, only a sample of people who live in Europe has been asked and, based on their answers, the writers of the article made an assumption about the whole population. So, what we have is a statistic.

When it comes to determining what you have in front of you, a parameter or a statistic, ask yourself, was it possible to survey an entire population that you see? If there’s a fact about thirty employees of a company or fifty couples, then it’s obvious that everyone has been actually surveyed. However, if the fact is about a very large population, such as all the residents of a city or all car owners, there’s no way that everyone has been asked. Therefore, in the first case, you have a parameter, and in the second one, you’re looking at a statistic.

Because a parameter is found out only when you know data about everyone in the population, it’s fixed. In contrast, a statistic that describes the same population can vary. This is because you can take different samples from the same population and thus get different results. So, a parameter is obviously more reliable than a statistic. Still, when a population is so large that nobody has the time or the resources to ask everyone, a statistic will provide enough information to draw conclusions.

### The distinction

If you are talking about a PARAMETER, you are talking about the whole population. On the other hand, a STATISTIC describes only a sample of the population.

The distinction lies not only in what they describe but also in their practical applications. While a parameter gives the true state of a population, a statistic provides an estimate of this state. Therefore, when researchers are unable to measure every individual in a population, they use statistics from a sample to infer the parameters.

### Tips to Remember the Differences

To better visualize these differences, consider the following table:

Aspect Parameter Statistic
Source Population (whole) Sample (subset)
Purpose Describe a population Estimate a parameter
Variability Fixed, but unknown Varies with sample

## Real-World Examples

In the field of statistics, parameters and statistics play pivotal roles in the analysis of data. These terms are not interchangeable, as they reference different aspects of data assessment. Here are real-world examples to illustrate the distinction:

• Average Height:
The average height of all adults living in a city would be considered a parameter because it’s a value that describes the entire population. In contrast, if one were to measure the average height of adults in a random sample from the city, this would be a statistic, as it only represents a subset of the population.
• Income Analysis:
An economist might refer to the mean income of every individual in a country as a parameter. However, surveys typically calculate the average income from a sample, yielding a statistic to infer about the whole population.
• Unemployment Rate:
The true rate of unemployment of a nation is a parameter; it’s a fixed aspect of the entire population. Nonetheless, government agencies use sampled data to estimate this value, which is then considered a statistic.

## Parameter vs. Statistic Examples

Parameter:

• Adjust the parameter to increase the volume.
• The study’s parameter limits its scope.
• Set the parameter for temperature control.
• The program crashed due to an invalid parameter.
• Define the parameter for the search query.
• The parameter determines the output quality.
• Change the parameter to alter the effect.

Statistic:

• The statistic shows a rise in employment rates.
• One statistic caught the researcher’s attention.
• That statistic is critical for our analysis.
• He quoted a statistic from the recent study.
• The statistic revealed a decrease in crime.
• A surprising statistic changed her perspective.
• The report was full of relevant statistics.

## Related Confused Words with Parameter or Statistic

### Parameter vs. Argument

In programming, parameters and arguments are closely related concepts that pertain to functions or methods, but they serve different roles:

Parameter:

• A parameter is a variable listed as part of a function’s definition.
• Parameters act as placeholders for values that a function can accept.
• When defining a function, you specify parameters to indicate what kind of input the function expects.

Argument:

• An argument is the actual value that is passed to the function when it is called.
• Arguments are the data you provide to the function’s parameters when invoking the function.
• When calling a function, you supply arguments that the function will use in its execution.

### Parameter vs. Perimeter

“Parameter” and “perimeter” are two distinct terms that are used in different contexts:

Parameter:

• In mathematics and statistics, a parameter is a quantity that influences the output or behavior of a mathematical function or statistical model but is not itself a variable of the function. For example, in the function f(x) = ax^2, “a” is a parameter that shapes the graph of the function.
• In programming and engineering, a parameter refers to a named variable used in a function or procedure to refer to one of the pieces of data provided as input.

Perimeter:

• The perimeter is a term used in geometry to describe the total length of the edges or boundaries of a two-dimensional shape. For example, the perimeter of a rectangle is calculated as the sum of the lengths of all four sides.
• In a more general sense, the perimeter can also refer to the border or outer boundary of a physical area or object.

## Parameter vs. Statistic: Practice and Exercises

Worksheet: Understanding the Differences Between a Parameter and a Statistic

Instructions: Read each of the following sentences carefully. Then, choose whether the numerical value mentioned is a Parameter or a Statistic. Write your answer in the space provided.

1. The average height of all the students in a large university is 168 cm. Answer: __________
2. In a survey of 200 households, 60% have internet access. Answer: __________
3. The proportion of left-handed people in the entire global population is 10%. Answer: __________
4. The median income of the sample of 500 families from a city is \$45,000. Answer: __________
5. The unemployment rate in a country last year was 5%. Answer: __________
6. Based on a sample of 1,000 voters in a town, 55% favor candidate A for mayor. Answer: __________
7. The true variance of the IQ scores in the entire population is 15 points. Answer: __________
8. A study reports that the average number of hours spent on homework by 10th graders in a particular school is 2 hours per night. Answer: __________
9. The probability of developing a certain disease in a lifetime for people in a specific country is 20%. Answer: __________
10. In a random sample of 300 adults in a region, 12% are found to be vegetarian. Answer: __________

1. Parameter (The average height is referring to the entire population of students at the university.)
2. Statistic (This percentage is based on a survey, which is a sample of the total number of households.)
3. Parameter (This proportion is referring to the entire global population, not a sample.)
4. Statistic (The median income is calculated from a sample of families, not the entire population.)
5. Parameter (The unemployment rate is a measure of the entire country’s population for that year.)
6. Statistic (This percentage is based on a sample of voters, not the entire population of the town.)
7. Parameter (The variance mentioned is for the IQ scores of the entire population.)
8. Statistic (This average is based on the students of a particular school, which is a sample of all 10th graders.)
9. Parameter (The probability is a characteristic of the population of that specific country.)
10. Statistic (The percentage of vegetarians is calculated from a sample of the adult population in the region.)

Remember, a parameter is a numerical value that summarizes data for an entire population, while a statistic is a numerical value that summarizes data from a sample. This distinction is important in the field of statistics because parameters are often unknown and must be estimated using statistics derived from samples.

What distinguishes a sample statistic from a population parameter?

A sample statistic is a numerical measure that represents characteristics of a sample, which is a subset of the population. Conversely, a population parameter is a numerical value that describes a characteristic of an entire population.

Can you illustrate the difference between a parameter and a statistic with real-world examples?

Yes, a real-world example would be measuring the average height of all students in a university (a parameter) versus the average height of students in a single classroom (a statistic). The university represents the whole population, while the classroom represents a sample of that population.

How do parameters and statistics differ in their application within statistical analysis?

Parameters are often used when complete data of a population is available, providing a definitive measure. Statistics, on the other hand, are used when data is collected from a sample, and they serve as estimates to infer population parameters.

In what situations would you use a parameter instead of a statistic?

Parameters are used when one needs to define a characteristic of an entire population when it is possible to obtain data from every member of that population. Statistics are not as reliable in such comprehensive scenarios due to their nature as estimations based on samples.

How can one identify whether a numerical value is a statistic or a parameter?

To identify whether a numerical value is a statistic or a parameter, one should determine if the value describes a sample (statistic) or the entire population (parameter). The key factor is the coverage of the data – whether it includes the whole population or only a part.

Is standard deviation considered a parameter or a statistic, and why?

Standard deviation can be both a parameter and a statistic. When it describes the variability of an entire population, it’s a parameter. When calculated from sample data to estimate the population standard deviation, it’s a statistic.