# Difference Between Parameter and Statistic

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## Introduction

In statistics, the phrases parameter and statistic are often used, and they play an essential role in determining sample size. Although the phrases parameter and statistics may appear synonymous, they are not. The parameter implies a summary description of the target population's characteristics. In contrast, a statistic is a summary value of a small group of people, referred to as a sample. The parameter is calculated based on the population's unit measurements. On the other hand, the statistic is derived from the sampling elements' measurements. Furthermore, a parameter considers every individual in a population, whereas statistics considers the data it gets from a sample, not the entire population.

If you ask all of the employees at a plant what sort of lunch they like, and half of them reply with pasta, you have a parameter - pasta is preferred by 50% of the employees. On the other hand, because you can't question every male in the world about their lunch preferences, it's hard to count how many men enjoy spaghetti. You'd most likely poll a representative sample (a subset) of them in such an instance and extrapolate the results to the total male population. This takes us to the second type of metric, a statistic.

In statistics, a sample is a piece or subset of a population. The objective is to calculate a population parameter. You can take many samples from a population, and the statistic (result) obtained from each sample will alter based on the samples. It's crucial to understand the notion and distinction between parameters and statistics when studying statistics, as they're frequently confused.

## Parameter vs. Statistic

A parameter is a value used to summarise data for an entire population. In contrast, statistics is a value used to summarise data from a sample, a subset of the total population parameter that differs from a statistic. A parameter is a fixed measure that describes the whole population. In contrast, a statistic is a sample feature, a subset of the target population. A parameter is a known number and a variable that depends on the percentage of the population.

In contrast, a statistic is a known number and a variable that relies on the percentage of the population. A statistic is a quantitative assessment of a sample's characteristics, whereas a parameter is a descriptive measure of a population. A sample statistic is used as a population estimate, whereas a parameter is an actual value obtained in a population. Symbol For a population, the parameter average or mean is represented by, whereas for a sample, it is represented by x.The parameter variance for a population is two as a statistic, whereas s2 represents it as a statistic for a sample. For a population, the parameter standard deviation is denoted by s, denoted by σ. The parameter N represents the size of a population, whereas n represents the size of a sample.

## Difference Between Parameter And Statistic In Tabular Form

 PARAMETERS OF COMPARISON PARAMETER STATISTICS MEANING A meter is a descriptive population measure. A statistic is a numerical figure that describes a population proportion. A statistic is a sample descriptive measure. A parameter is a metric that describes a population. MEASURE Measuring a parameter is nearly impossible. It is always possible to measure a statistic. NUMERIC VALUE The outcome of the argument has a fixed value. The outcome of statistics is likely to differ depending on the size of the population. STANDARD DEVIATION A population's standard deviation is indicated as σ. A sample's standard deviation is denoted by the letter s. PARAMETER Σ2 represents a population's variance. s2 is used to express the variance of a sample. POPULATION SIZE N is the parameter that determines the size of a population. The statistic n determines the size of a sample. SYMBOL The population's mean or average is indicated by µ. The letter x̅ denotes the mean or average of a sample. SUITABLE It is inconvenient to utilize for a significant population, primarily if all units are unable to be located. Even if you can't find all of the units, it's convenient for a vast population. SURVEY COST . The cost of conducting the survey is lower. RESULTS It produces the natural outcome in terms of specified features. As a consequence, it produces the most likely estimate for specified attributes.

## What Is Parameter?

The parameter is a fixed population feature based on all of the population's members. As a result of his method, the cost of the survey raises. The term "population" here refers to a grouping of all the units under examination that have similar features. Because every member of the population is polled to determine the parameter, it is a numerical number that remains constant. It denotes the actual figure, which is determined after the completed census. A parameter is a numerical number that describes the characteristics of a population as a whole. The parameter is practically hard to determine, especially in the event of a significant population.

The identified parameter can easily be for a tiny population since the location of each individual can be with absolute confidence. Calculating a parameter becomes simple when all people can be discovered and measured without missing one.

The symbol for parameter denotes a variety of signals, such as mean, variance, and standard deviation. The letter N is a parameter used to reflect the total population size. This is for a group of people. These numbers are derived from a sample that is supposed to represent the population.

Some Example Of Parameters are :

• A metric that may be calculated is the amount of calcium in the diet of all middle school pupils daily for a specific school. In this situation, every middle school student is tallied, and the acquired data may be without leaving out a single child from the population.
• Another parameter example is the number of TB cases reported in a specific set of hospitals over a particular time. In this instance, too, every population unit is wholly accounted for.

## Most Common Type of Parameters

As we have learned about the definition of a parameter, there are also some common types of parameters which are listed below:

### 1. Mean

The mean, often known as the average, is the most widely used of the three measures of central tendency. Researchers use the parameter to define the data distribution of ratios and intervals. The mean is calculated by adding the values and dividing them by the number of scores.

### 2. Median

The median is used to compute variables measured on an ordinal, interval, or ratio scale. It is calculated by sorting the data from lowest to highest and selecting the number(s) in the center. When there are many odd data points, the median is generally the middle number. When the numbers are even, the median is calculated by adding the two intermediate values and dividing them by two and get the mean.

### 3. Mode

The mode is the most frequently occurring number in a data distribution. It demonstrates which number or value is the most numerous or prevalent in the data distribution. The mode applies to any form of data.

## What Is Statistic?

A statistic is a numerical number calculated from a sample of data. It's a descriptive statistical measure and sample observation function. A sample is a population subset that accurately represents the entire population in all aspects. The most typical use of statistics is to estimate a population parameter.

Multiple samples can be drawn from a particular population, and the results (statistics) obtained from various samples will change depending on the samples.

A statistic is a figure that only considers a small portion of the whole population. It is based on a representative sample. A statistic is a parameter estimate. It might be the outcome of random sampling or predetermined criteria for selecting a sample. Sampling is a method of gathering information or statistics for a population without measuring every person in the population. The sampling method is required because it is practically impossible to measure or count every individual in a community, especially when populations are enormous and it isn't easy to find information on every individual.

With symbols such as x for the mean, s2 for the variance, and s for the standard deviation, parameters can provide some indicators. The letter n is a parameter that represents the total size of the sample. These figures are derived from a population-representative sample.

Some Examples Of Statistics:

• One figure is the number of persons who believe it is preferable to use the public bus to work rather than the local railway. Because it is impractical or impossible to poll every single individual, the opinion of a sample is taken into account. The remaining information is extracted from the patterns in the data.
• Another statistic to consider is the number of people who prefer an evening stroll over a morning walk. Again, taking into consideration, every single individual will result in a massive amount of data that will be impossible to deal with. Therefore, it is preferable to collect the views of a representative population sample.

The following two categories are used to categorize statistics.

• Descriptive Statistics
• Inferential Statistics

Descriptive Statistics: The data is summarised and explained in descriptive statistics. The summarization is done from a population sample utilizing the mean and standard deviation factors. Descriptive statistics are a means of organizing, representing, and explaining a collection of data using charts, graphs, and summary measurements.

• Histograms, pie charts, bars, and scatter plots are common ways to summarise data and present it in tables or graphs.
• Descriptive statistics are just that: descriptive. They don't need to be normalized beyond the data collected.

Inferential Statistics: We attempt to interpret the Meaning of descriptive statistics in Inferential Statistics. We utilize Inferential Statistics to convey the Meaning of the acquired data after it has been gathered, evaluated, and summarised.

• For testing hypotheses, inferential statistics are utilized and study correlations between variables and make demographic projections. In addition, inferential statistics are used to derive conclusions and inferences from samples, i.e., to make reliable generalizations

## Main Differences Between Parameter And Statistics in Points

The distinction between statistic and parameter is evident on the following grounds:

• A statistic is a feature of a tiny subset of the population, i.e., a sample. The parameter is a fixed metric that describes the population under consideration.
• The statistic is a changeable and known number that depends on a population sample, whereas the parameter is a fixed  unknown numerical value
• .A parameter is an example of a population measure, whereas a statistic is an example of a sample measure.
• A parameter is a computed real value for a population, whereas a sample statistic is used to produce an estimate for a population.
• A parameter is virtually hard to measure, but a statistic is simple to calculate.
• The parameter for population size is represented by the letter N, whereas the letter n represents the statistic for sample size.
• A population's parameter variance is denoted by σ2, but s2 denotes a sample variance.
• The parameter yields a constant answer, but the statistics yield a variable result based on population size.
• It takes less time to survey to calculate the parameter but more time to survey to calculate the statistics.

## Conclusion

To summarise the subject, it is vital to understand that the numerical value derived from the population is known as the parameter. The numerical value is a statistic if a sample produces the result. Even though they are two different numerical quantities, parameters and statistics are frequently confused. The parameter considers the entire population, whereas statistics considers a portion of it. Therefore, the most probable estimate is given by parameter. Statisticians, on the other hand, provide the natural outcome. Statistics is a numerical number determined from a particular sample, whereas a parameter is a numerical value obtained from a population. A parameter's result is fixed. On the other hand, the outcome of statistics changes depending on the size of the population.

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"Difference Between Parameter and Statistic." Diffzy.com, 2022. Tue. 24 May. 2022. <https://www.diffzy.com/article/difference-between-parameter-and-statistic-60>.

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