What is the difference between sample and parameter?

The parameter is drawn from the measurements of units in the population. As against this, the statistic is drawn from the measurement of the elements of the sample.

While studying statistics it is important to the concept and difference between parameter and statistic, as these are commonly misconstrued.

Content: Statistic Vs Parameter

1. Comparison Chart
2. Definition
3. Key Differences
4. Illustration
5. Conclusion

Comparison Chart

Basis for ComparisonStatisticParameterMeaningStatistic is a measure which describes a fraction of population.Parameter refers to a measure which describes population.Numerical valueVariable and KnownFixed and UnknownStatistical Notationx̄ = Sample Meanμ = Population Means = Sample Standard Deviationσ = Population Standard Deviationp̂ = Sample ProportionP = Population Proportionx = Data ElementsX = Data Elementsn = Size of sampleN = Size of Populationr = Correlation coefficientρ = Correlation coefficient

Definition of Statistic

A statistic is defined as a numerical value, which is obtained from a sample of data. It is a descriptive statistical measure and function of sample observation. A sample is described as a fraction of the population, which represents the entire population in all its characteristics. The common use of statistic is to estimate a particular population parameter.

From the given population, it is possible to draw multiple samples, and the result (statistic) obtained from different samples will vary, which depends on the samples.

Definition of Parameter

A fixed characteristic of population based on all the elements of the population is termed as the parameter. Here population refers to an aggregate of all units under consideration, which share common characteristics. It is a numerical value that remains unchanged, as every member of the population is surveyed to know the parameter. It indicates true value, which is obtained after the census is conducted.

Key Differences Between Statistic and Parameter

The difference between statistic and parameter can be drawn clearly on the following grounds:

1. A statistic is a characteristic of a small part of the population, i.e. sample. The parameter is a fixed measure which describes the target population.
2. The statistic is a variable and known number which depend on the sample of the population while the parameter is a fixed and unknown numerical value.
3. Statistical notations are different for population parameters and sample statistics, which are given as under:
   • In population parameter, µ (Greek letter mu) represents mean, P denotes population proportion, standard deviation is labeled as σ (Greek letter sigma), variance is represented by σ2, population size is indicated by N, Standard error of mean is represented by σx̄, standard error of proportion is labeled as σp, standardized variate (z) is represented by (X-µ)/σ, Coefficient of variation is denoted by σ/µ.
   • In sample statistics, x̄ (x-bar) represents mean, p̂ (p-hat) denotes sample proportion, standard deviation is labeled as s, variance is represented by s2, n denotes sample size, Standard error of mean is represented by sx̄, standard error of proportion is labeled as sp, standardized variate (z) is represented by (x-x̄)/s, Coefficient of variation is denoted by s/(x̄)

Illustration

1. A researcher wants to know the average weight of females aged 22 years or older in India. The researcher obtains the average weight of 54 kg, from a random sample of 40 females.
   Solution: In the given situation, the statistics are the average weight of 54 kg, calculated from a simple random sample of 40 females, in India while the parameter is the mean weight of all females aged 22 years or older.
2. A researcher wants to estimate the average amount of water consumed by male teenagers in a day. From a simple random sample of 55 male teens the researcher obtains an average of 1.5 litres of water.
   Solution: In this question, the parameter is the average amount of water consumed by all male teenagers, in a day whereas the statistic is the average 1.5 litres of water consumed in a day by male teens, obtained from a simple random sample of 55 male teens.

Conclusion

To sum up the discussion, it is important to note that when the result obtained from the population, the numerical value is known as the parameter. While, if the result is obtained from the sample, the numerical value is called statistic.

A statistic and a parameter are very similar. They are both descriptions of groups, like “50% of dog owners prefer X Brand dog food.” The difference between a statistic and a parameter is that statistics describe a sample. A parameter describes an entire population.

Watch the video or read the steps below:

How to tell the difference between a statistic vs parameter

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For example, you randomly poll voters in an election. You find that 55% of the population plans to vote for candidate A. That is a statistic. Why? You only asked a sample—a small percentage— of the population who they are voting for. You calculated what the population was likely to do based on the sample.

Censuses result in a parameter about the population.

You could ask a class of third graders who likes vanilla ice cream. 90% raise their hands. You have a parameter: 90% of that class likes vanilla ice cream. You know this because you asked everyone in the class.

Steps to tell the difference between a statistic and a parameter:

Step 1: Ask yourself, is this a fact about the whole population? Sometimes that’s easy to figure out. For example, with small populations, you usually have a parameter because the groups are small enough to measure:

Examples of parameters:

• 10% of US senators voted for a particular measure. There are only 100 US Senators, you can count what every single one of them voted.
• 40% of 1,211 students at a particular elementary school got below a 3 on a standardized test. You know this because you have each and every students’ test score.
• 33% of 120 workers at a particular bike factory were paid less than $20,000 per year. You have the payroll data for all of the workers.

Step 2: Ask yourself, is this obviously a fact about a very large population? If it is, you have a statistic.

Examples of statistics:

• 60% of US residents agree with the latest health care proposal. It’s not possible to actually ask hundreds of millions of people whether they agree. Researchers have to just take samples and calculate the rest.
• 45% of Jacksonville, Florida residents report that they have been to at least one Jaguars game. It’s very doubtful that anyone polled in excess of a million people for this data. They took a sample, so they have a statistic.
• 30% of dog owners poop scoop after their dog. It’s impossible to survey all dog owners—no one keeps an accurate track of exactly how many people own dogs. This data had to be from a sample, so it’s a statistic.

If in doubt, think about the time and cost involved in surveying an entire population. If you can’t imagine anyone wanting to spend the time or the money to survey a large number (or impossible number) in a certain group, then you almost certainly are looking at a statistic.

Like the explanation? Check out the Practically Cheating Statistics Handbook, which has hundreds more step-by-step explanations, just like this one!

What's the difference between a parameter and a sample?

Revised on November 18, 2022. A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

What is the difference between a sample and a population parameter?

sample statistic. When you collect data from a population or a sample, there are various measurements and numbers you can calculate from the data. A parameter is a measure that describes the whole population. A statistic is a measure that describes the sample.

What is an example of a parameter?

A parameter is used to describe the entire population being studied. For example, we want to know the average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.

Is sample size a parameter?

Sure, sample size is a statistic. A “parameter” is a knob you turn to get some distribution to behave a certain way.