Parameters Vs. Statistics: 12 Differences & Examples

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What Is A Parameter?

Parameter in statistic is any numerical quantity that characterizes a given population or some aspect of it.  When we make inference, the parameter is not known because it is impossible to collect data from everyone in the population.  In this regard, we use a statistic of a sample picked from the population to derive a conclusion about the parameter.  

For example, the parameter can be used to describe the mean amount of salaries paid to the workers of XYZ organization. Assuming that the population of workers in the organization is 1200, the researcher can begin by calculating the salary of a few select samples of the population or about 10 workers. For three samples of 10 workers each, the researcher may obtain a mean of $ 1500, $1200 and $700. The researcher can use this sample mean to make an inference about the population parameter.

The most common used parameters are measures of central tendency. The measures include mean, median and mode and they are used to describe how data behaves in a distribution.

  • Mean is the average of variables
  • Median is obtained by arranging the data from the lowest to the highest and then picking the number (s) at the middle.
  • Mode is the most occurring number within a data distribution.

Also Read: Difference Between Inferential And Descriptive Statistics

What You Need To Know About Parameter

  1. A parameter is a fixed measure describing the whole population (population being a group of people, things, animals, animals, phenomena that share common characteristics).
  2. A parameter is calculated in a small, closed population in which every individual can be located and measured.
  3. A parameter is fixed, unknown numerical value.
  4. Parameter is not always possible to measure, especially in an area where there are too many individuals and locating all individual is not possible.
  5. The parameter average or mean for a population is indicated with µ.
  6. The parameter variance for a population is indicated with σ2
  7. The parameter standard deviation for a population is indicated with σ.
  8. The parameter’s correlation coefficient is indicated by Þ.
  9. The parameter for the size of a population is given by N.
  10. Parameter requires less time to conduct the survey.
  11. A parameter gives the most probable estimate as a result concerning specific characteristics.
  12. Parameter is convenient to use for a large population, even if you cannot locate all units.

Examples Of Parameters:

  • 60% of US members of house of representative voted to approve an impeachment motion against President Donald Trump. There are only 435 members of house of representative. Therefore, it is easy to calculate the number of those who voted for and against the impeachment motion.
  • 80% of 320 students of Bachelor of Science Accountancy at Harvard University graduated with Second Class Honors Upper Division. In this case you can get the exact number of students who graduated with Second Class Honors Upper Division, which is 256.
  • 40% of 780 workers of an XYZ manufacturing company are paid less than $34000 per year.

What Is A Statistic?

Statistics are numbers that summarize data from a sample i.e some subset of the entire population.  For instance, suppose we select a random sample of 300 students from a school of 2000 students. The average grade point would be an example of a statistic. So would be the average height. In fact, any measurable characteristic from the sample (300 students) would be an example of a statistics.

When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose. For example:

  • In descriptive statistics, a descriptive statistics is used to describe the data
  • In estimation theory, an estimator is used to estimate a parameter of the distribution (population).
  • In statistical hypothesis testing, a test statistics is used to test a hypothesis.

What You Need To Know About Statistic

  1. A statistic is characteristic of a sample, a portion of the target population.
  2. A statistics is carried out in a large open population in which it is not possible to locate every individual.
  3. Statistics is a known number and a variable which depends on the portion of the population.
  4. A statistics is always possible to measure.
  5. Average or mean of a statistics can be indicated with ẋ.
  6. The statistics variance for a sample is indicated with S2
  7. The statistics standard deviation for a sample is indicated with s.
  8. A statistic’s correlation is indicated by r.
  9. Statistics representing the size of a sample is given by n.
  10. Statistics require more time to conduct the survey.
  11. Statistics gives a less accurate result with regard to specific characteristics.
  12. It may prove tedious and not convenient

Examples Of Statistics

  • 60% of UK residents agree with the latest EU immigration policy. Well, it is not possible to actually ask every resident of the UK whether they agree. The researcher will just have to take samples and calculate the rest.
  • 18% of Women in Abington, Massachusetts report that they have experienced gender violence. In this regard, the researcher did not ask thousands of women in Abington for this data. They literally took a sample and therefore they have a statistics.
  • 33% of residents of New Hampshire are in formal employment. Well, it is impossible that a researcher polled in excess of a million people for this data. This data is from a sample, therefore it is a statistics.

Also Read: Difference Between Bar Graph And Histogram

Difference Between Parameter And Statistics In Tabular Form

BASIS OF COMPARISON PARAMETER STATISTICS
Description A parameter is a fixed measure describing the whole population (population being a group of people, things, animals, animals, phenomena that share common characteristics).   A statistic is characteristic of a sample, a portion of the target population.  
How It Is Conducted A parameter is calculated in a small, closed population in which every individual can be located and measured.   A statistics is carried out in a large open population in which it is not possible to locate every individual.  
Nature A parameter is fixed, unknown numerical value.   Statistics is a known number and a variable which depends on the portion of the population.  
Measurement Parameter is not always possible to measure, especially in an area where there are too many individuals and locating all individual is not possible.   A statistics is always possible to measure.  
Average/mean The parameter average or mean for a population is indicated with µ.   Average or mean of a statistics can be indicated with ẋ.  
Variance The parameter variance for a population is indicated with σ2   The statistics variance for a sample is indicated with S2  
Standard Deviation The parameter standard deviation for a population is indicated with σ.   The statistics standard deviation for a sample is indicated with s.  
Correlation The parameter’s correlation coefficient is indicated by Þ.   A statistic’s correlation is indicated by r.  
Size Of Sample The parameter for the size of a population is given by N.   Statistics representing the size of a sample is given by n.  
Survey It requires less time to conduct the survey.   It require more time to conduct the survey.  
Accuracy It gives the most probable estimate as a result concerning specific characteristics.   It gives a less accurate result with regard to specific characteristics.  
Convenience It is convenient to use for a large population, even if you cannot locate all units.   It may prove tedious and not convenient  

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