Parameter vs. Statistic: 3 Areas of Difference

A parameter is essentially a statistic that accurately and literally reports information about an entire population. As such, population parameters must take in data from every single member of a population with no exceptions. When this is impossible, people use sampling methods to obtain reliable statistics instead.

A statistic is a sample proportion of a given population, rather than a literal accounting of every member of the population group. By taking a characteristic of a sample, statisticians sidestep the need to survey impossibly large numbers of people.

So long as statisticians obtain a representative sample of the population—one that reflects the demographics, viewpoints, and more of the actual population—they are likely to achieve a similarly high level of accuracy with their research.

There are two main fields of statistics: descriptive statistics (statistics that use descriptive measures to convey mathematical truths about the data’s measures of central tendency—mean, median, mode, etc.) and inferential statistics (statistics people use to infer and make educated guesses about broader trends the data suggests).

Parameters and statistics have a fair amount in common, but it’s important to know what sets them apart. Here are three areas of major difference between the two concepts:

1. 1. Accuracy: While parameters and statistics can both be quite accurate, parameters will always be the most accurate. This is because they directly survey every possible member of a population group, whereas sample statistics only survey representative members of that group. The latter must make statistical inferences, whereas the former can literally express data about an entire group. Still, statistics can lie within the same confidence interval as parameters, so long as those who are building out these data sets mitigate against standard errors in polling.
2. 2. Notation: Examples of parameters are more likely to feature Greek letters like lowercase sigma (σ) or mu (µ). Examples of statistics are more likely to feature Latin letters like p-hat (p̂) or x-bar (x̄).
3. 3. Sample size: Parameters survey an entire group of people, whereas statistics use a smaller sampling distribution to arrive at similar data inferences. As a result, it’s easier to produce a parameter for a small population size and a statistic for a large population size.

Consider these four examples of situations in which you might use a parameter or a statistic in the real world:

1. 1. Customer satisfaction: Companies want to excel by appealing to their customers, so suppose one wants to see how much their consumer base enjoys a new product. They could aim to take a parameter of every customer who’s bought the item, but this would be very difficult to achieve in actual practice. In this event, they might settle for a simple random sample to provide an unbiased estimate of customer satisfaction (or dissatisfaction) instead.
2. 2. Demographic data: Consider a census taker hoping to ascertain the mean height of every person in their country. To obtain this demographic data set, they will have all the resources of their country’s government behind them to actually obtain a parameter of all members of the population. Still, some people might slide through the cracks. As an insurance policy, the census taker could compare their parameter results against a sample size statistic to see if the height data more or less matches.
3. 3. Educational success: At a single high school, it would be fairly easy to discern the numerical value of the entire student body’s mean GPA. This would become much more difficult to do if you wanted to take in data from every single high school in the country. In that scenario, a smaller population proportion (or statistic) could attain a sample mean to infer broader conclusions.
4. 4. Political issues: Pollsters would ideally be able to take a common parameter for the whole country’s population to learn how all citizens feel about a given political issue. Unfortunately, obtaining such a population mean (or average) opinion is nigh on impossible. Instead, they take sample data from a subset of the entire population and use statistical analysis to make an educated guess about what those whom they didn’t poll would say, too.

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