When working with data, you'll often encounter different types of data. So we're going to now look at some of those types of data, the more common ones that you'll encounter in particular in this class. So the first thing I want to talk about is a parameter versus a statistic.
A parameter is some numerical measurement describing a characteristic of a population. So, for example, it might be talking about the mean of heights of people, or possibly the number of M&Ms in a fun-sized M&M pack. So a parameter is that measurement describing the characteristic of the entire population.
And a statistic is some numerical measure measurement describing some characteristic of a sample that comes from a larger population. So a sample is just a small part of the larger population, and when we talk about a statistic, we're talking about some numerical measurement of that smaller sample. So we'll often encounter quantitative data and also qualitative data, and so it's important to know the difference between the two. Quantitative data consists of numbers, and those numbers could either represent counts or measurements, whereas qualitative data, which is also called categorical data, or less often, attribute data, consists of names or labels that are not numbers. Now this is a little, there's a little more to this.
We could have our categories be numbers, but those numbers would not represent counts or measurements if it's qualitative data. So we'll see some examples of that. So you do have to be a little careful in distinguishing between quantitative and qualitative. Now quantitative data, that is the ones that represent counts or measurements, the numbers that represent counts or measurements, can come in either discrete data or continuous data. So you can get discrete data when the number of possible values you can get from your data is finite or countable.
So for example, if you roll a pair of dice, the only possible values when you add the... the two up numbers together, the only possible values are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12. So this is a finite list of numbers, which means this is discrete data. Countable just means a list of numbers that is infinite, so not finite, but that list can be arranged in order.
So, for example, if I could either get a list such as 3, 6, 9, 12, 15, 18, 21, or even negatives are fine, negative 8, negative 1, 0, 15, etc., So continuous data is numbers that can take on any value between any two numbers. So for example, if we're measuring the amount of milk that cows produce, you could get 2 liters or 3 liters of milk, but you could also get any decimal number in between those, such as 2.37 liters or 2.81932855 liters. So notice with the dice example we saw previously, we couldn't get a number such as 3.8721. We could only get 3, 4, 5, or 6. But when we're measuring liters, we could get anything in between 2 or 3 or anything between 3 and 4. So don't make the mistake of thinking it's just because we have decimals. The idea that separates discrete and continuous data is that any number between two numbers could come up.
So we're allowed to have decimals for discrete data, but we would be limited to certain decimals. We wouldn't be able to get any decimal. Another way to classify data is into four levels of measurement. We'll have the nominal level at the base, or the most basic level of measurement, and then the ordinal level of measurement, then the interval level of measurement, and the ratio level of measurement.
Now it's important to note that each level of measurement takes on all the information that the previous level of measurement would have. So if we have data at the interval level of measurement, it is also data that takes on the information at the ordinal and nominal level of measurement. So let's look at some examples.
At the nominal level of measurement, data consists of names, labels, or categories, but no numbers. The data cannot be arranged in any kind of meaningful order, and that's the important part about the nominal level. So, for example, if you ask people, what is your political party affiliation, the responses will be Democrat, Republican, Independent, or some other response. We cannot order this data in any meaningful way. Ordinal level of measurement, data are at this level if it can be arranged in some meaningful order, but differences between two different pieces of data cannot be determined or are meaningless.
So for example, on our first exam, suppose Wilma gets an A and Spencer gets a B. So because we can order these, clearly an A is better than a B, so I would order these as A first and then B. We can order them, but we can't subtract A minus B and get some sort of meaningful difference.
Data are at the interval level of measurement if we can find a difference that does matter between data, but there's no natural zero starting point, or rather, zero is not the natural zero starting point. starting point. So for example, if Bob was born in 1979 and Jamie was born in 1995, if we take their difference we can find out how much older Bob is than Jamie.
Jamie, but the year zero is not the natural zero starting point. So we wouldn't find the ratio between these two years because the ratio would be meaningless. But the difference between these two years does give us interesting information, namely how much older Bob is than Jamie.
Data is at the ratio level of measurement if differences are meaningful, so the same as the interval level of measurement, but there is a natural zero starting point, or in other words, zero is the absolute zero. It's the natural zero starting point. So for example, the amount you pay for gas when you fill up your tank, you can pay zero dollars if you fill up your tank with zero amount of gas, zero gallons, and then from there it goes up.
But since we can't go below zero, in other words, we wouldn't pay negative money for negative gas, Zero is the natural zero starting point, and so this level of data is at the ratio. So try this on your own. Pause the video here.
But try to match the terms on the left with the correct definitions on the right. So here's the answer to that question.