Unit 8 Introcontinued

Unit 8 IntroContinued

Parameter vs Statistic

Any measure of the population is called a parameter. For example, the average inside diameter of an entire shipment of washers would be an example of a parameter. We usually use the Greek letter mu, as the symbol for the population average, also known as the mean. When we take a sample from the population and find some measure of the sample, such as the average weight of the sample, we call that measure a statistic. The average of a sample is denoted as We are going to learn about some other measures, but just remember, when they are measures of a population they are called parameters, and when they are the measures of a sample, they are called statistics.

Question #1
Distinguish between a parameter and a statistic.

Data

In this course, we are only going to focus on two types of data, discrete and continuous. Discrete data is easy to understand. When we count the number of marbles in a bag or the number of students in a classroom, we get a discrete number. There cannot be 18.8091 marbles in a bag, although I understand that there are 2.5 children in the average American family. If a set of numbers is countable, then they are discrete. Other examples include the leaves on a tree and the blades of grass in a lawn. These may be very large numbers, but size is not a defining characteristic for a set to be discrete. A related kind of data is called categorical. Things like color, red, blue, etc. is an example of categorical data.

Continuous numbers are more difficult to understand because they are really a mathematical abstraction. To fully understand the concept of continuity, you would need to know calculus. Rather than defining the concept of continuity, let’s just consider some of its properties and how continuous numbers compare to countable numbers.

Consider your height. You may think you are exactly so many inches tall, say 65.5 inches, but in reality that is an approximation based on the accuracy of the measuring device. With a more accurate device you might see that your height is really 65.52 inches, and then with an even more accurate device, you would see that it’s 65.518 inches, and so on. In theory, we could always keep adding decimal places. The process never ends, and the decimal places go on forever. Hence, you would never be able say exactly how tall you are. That is the nature of a continuous number.

Question #2.
Distinguish between discrete and continuous data.

As a general rule of thumb, anytime you use a device, such as a ruler or a timer, to make a measurement, that measurement is going to be a continuous number. If you are counting, then the data is discrete.

Another interesting difference between discrete and continuous numbers is proximity. The discrete integer 3 is right next to 4. There are no discrete integers between those two. However, you could never find two continuous numbers right next to each without any continuous numbers between them. For example, if A and B are continuous numbers that are claimed to be right next to each other, (A+B)/2 would be a continuous number between them. This will always be true. For this reason, we graphically represent discrete numbers as dots on the graph and continuous numbers as a solid line.

Statistical Significance

A result is considered to be statistically significant if the likelihood of getting the result purely by chance is small, typically 5% or less. For example, let’s say we were measuring the inside diameter of a shipment of washers. The manufacturer claims that the average inside diameter is 25.00 mm. Out of a shipment of 50,000 washers, we sample 40, measure their inside diameters, and find the average to be 24.75 mm. If the population inside diameter really was 25.00 mm, it can be shown using statistical methods that the chances of our selecting a simple random sample of 40 washers whose average inside diameter measured 24.75 mm was less than 1%. Now think about that result. Yes, we could have just picked a fluke sample, but the chances of our doing so are less than one percent. Now, which is more likely, the fact that we selected a near magical sample or that the manufacturer is mistaken?

This is what we mean by statistically significant. The likelihood of our selecting such a fluke sample purely by chance is so small, the difference we found is considered to bestatistically significant. This is a fundamental concept in Statistics, so be sure you understand it.

Question #3
Determine if a result is statistically significant.

Question #4
Categorical data.

This is the end of Unit 8. Turn now to your MyMathLab homework to get more practice with these concepts.