Which of the following best describes the difference between parameters and statistics?

Before you start, you may want to read these overviews:
What is a Statistic?
What is a Parameter?

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

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.

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!

References

Dodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.
Gonick, L. (1993). The Cartoon Guide to Statistics. HarperPerennial.
Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences, Wiley.
Lindstrom, D. (2010). Schaum’s Easy Outline of Statistics, Second Edition (Schaum’s Easy Outlines) 2nd Edition. McGraw-Hill Education
Wheelan, C. (2014). Naked Statistics. W. W. Norton & Company

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