# Parameter and Statistics

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at August 31st, 2021 , Revised On February 8, 2023We deal with these two terms in statistics a lot and often have a hard time differentiating them. If you are one of those people, you have come to the perfect place. This guide on statistics vs. parameters is the perfect rejoinder to all your skeptical thoughts.

**What are Parameter and Statistics in Research?**

**A parameter*** in statistics implies a summary description of the characteristic of an entire population based on all the elements within it.* For instance, all the children in one city, all female workers in a country, all the items in grocery stores globally, and so on.

Suppose you ask the students in a class what kind of lunch they prefer. Half of them might say fries, and half would say a burger or sandwich. Now the parameter here would be 50%. But can you count how many children in the whole world like fries or sandwiches? You sure cannot do that. If it is impossible to count or measure a value in such cases, you take a sample and assess the entire population based on it. So the sample here (children in the class) represents the entire population (children in the world).

On the other hand**, statistics***is a measure of a characteristic of a fraction or sample of the population under study*. It is basically a part or portion of a population. While the parameter is drawn from the measurements of units in the entire population, a sample is drawn from the measurement of elements from the sample.

For instance, if you are to find out the mean income of all the subscribers of a YouTube channel-a parameter of a population. You might simply draw some 150 subscribers and determine their mean income (a statistic). You would conclude that the average income of the entire population is the same value as the sample.

Here are a few more keynotes to make the differentiation between statistics and parameter:

**Parameter Vs Statistics**

- A parameter is fixed and unknown while the statistics is a variable and known number
- Parameter describes the whole population and statistics describes a portion of the population
- Sample statistics and population parameters have different statistical notations. For example, in population parameter, mean is represented by µ (Greek letter mu). While in sample statistics, mean is represented by p̂ (p-hat)
- Statistics is used to get the actual outcome with respect to a certain characteristic and parameter is used to get the most possible estimated outcome
- Statistics is not appropriate if the data is huge while parameter is great for large scale data
- Statistics is time-consuming and parameter comparatively can be quick
- Parameter is more reliable, and dependable on the survey and statistics is less dependable on the survey
- Statistic is pricy while parameter does not need harsh money

Below are a list of examples of both for further clarification.

**Examples of Parameters:**

- Median income of all the females in Atlanta
- Standard deviation of all the rice farms in the city
- Proportion of all the schools in the world

**Examples of Statistics:**

- Median income of 1050 females in Georgia
- Standard deviation of one rice farm in the city
- Proportion of all the schools in one region

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**Statistical Notation of Parameter and Statistics**

Statistics | Parameter |
---|---|

x̄ = Sample Mean | μ = Population Mean |

s = Sample Standard Deviation | σ = Population Standard Deviation |

p̂ = Sample Proportion | P = Population Proportion |

x = Data Elements | X = Data Elements. |

n = Size of sample | N = Size of Population |

r = Correlation coefficient | ρ = Correlation coefficient |

**Interpreting Study Results with Statistics and Parameters**

When assessing the outcomes of research or study, you sure can be confident that parameters influence factors relevant to every person, object, and circumstance within a given population.

However, with statistics, it is imperative to keep in mind how the sample was collected in the first place. You must see if the sample is an accurate representation of the entire population. Only then would you be able to generalize conclusions for the whole population. A random sample here is most probably a good representative of a population.

Another thing to take into consideration while interpreting data is understanding what the numbers represent instead of just knowing what numerical calculations you have at hand. If the data is parameters, you must ensure that they are descriptive of the given population. And, if the data you are provided with is statistics, you must pay attention more than required and take as much time as you need because this is the tricky one.

In the meantime, if you have any confusion or queries, please let us know by commenting below

**FAQs About Parameters and Statistics**

A parameter is a number that describes the whole population. For example, all the boys in the world.

A statistic is a number that describes a sample from a population under study.

Sample are used to make inferences or conclusions about different populations. Sample are a lot easier to collect information/data because they are manageable and cost effective.

The sign ** μ** refers to a population mean while

**refers to the standard deviation of a population.**

*σ*s2 is used for representing sample variance and X ~ is used to show the distribution of random variable X