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# Types of Data in Statistics, Some Examples, and Statistics Definitions (Intro to Stats)

## Types of Data

Parameter – this is always a numerical measurement which describes a characteristic of a population.

Statistic – this is always a numerical measurement which describes a characteristic of a sample.

Though these both may sound similar, a parameter and statistic are not the same at all except for the fact they are both numerical measurements. Since they sound similar it would prove wise to provide a couple of examples to make sure we understand the difference between the 2.

Take into consideration the congress of the United States, we can see there are so many men and so many women. If we are talking about the entire group of congress, that would be a parameter.

A statistic would deal with, for example, the average amount of time one may spend waiting to check out at the grocery store. This would require only a sample of people waiting as opposed to a parameter which describes a population, not a sample.

Quantitative data -data which consists always of numbers which represent counts or measurements.

Qualitative data – this is data which consists and is distinguished by any non-numerical characteristic. It is also referred to commonly as categorical or attributes data).

Discrete data – this type of data results when the amount of possible values is a countable or a finite number. (So the number of possible values would be something like 0, 1, 2, and continue forward so on and so on.

Continuous (numerical) data – this data results from values whos possibilities are infinite. These values correspond to a continuous scale which covers ranges of values with no gaps, jumps, or interruptions.

### Example and Difference Between Continuous Data and Discrete Data

If several sets of data, would they all be considered the same? Let’s look at an example to better understand the difference between discrete data and continuous (numerical) data.

For discrete data, let us picture counting the average eggs a chicken hatches. This number at the end of the day will be a number such as 1, 2, 3, etc.

For continuous data, let us picture milking a cow instead, and ending up with what we believe to be 2 gallons of milk, but really it could be something like 2.03, or better yet it might be something like 2.03111, in other words, it could take any value that is within a continuous range.

We counted for chicken eggs (that was discrete), but for cows milk, we measured it (that would be continuous).

## The 4 different levels of measurement (With examples)

So how would we break down the different data? We can use different levels of measurements. How do we take a particular data set and then try to determine its level of measurement? We should always start at the nominal level. Any data will satisfy the requirements of the nominal level.

The nominal level of measurement – this level is always characterized in data which consists of labels, names, or categories. This data can’t be arranged in any ordering scheme, such as high to low.

If we are looking at NBA player heights, the data would meet the first level of measurement since the data is height. Since it meets the nominal level, we would then check the ordinal level.

The ordinal level of measurement – this is when the data can be arranged in a specific order, but the differences between the values either are meaningless or can’t be determined. Such as in the question “rate your degree of discomfort, 1-not bad , 2-kind of bad, or 3- bad”. In this example, the numbers are only used as tags.

Can we arrange the data in a meaningful order regarding NBA player heights? With height, we are able to arrange the data from shortest to tallest, or tallest to shortest. This means it satisfies the ordinal level which means we can ignore the nominal level since that is the lowest level. The next level we want to look at is the interval level.

Then we have the interval level of measurement – this is similar to the ordinal level, the addition would be that the differences between 2 values of data are meaningful. (Data that is at this level doesn’t have a natural zero starting point or in other words, where none of the quantity is present.)

Do our heights satisfy this? If we have a height of 5’6 and another of 5’12, then the data between those 2 values are meaningful. This data type (heights) also satisfies the interval level of measurement. The last and highest possible level is the ratio level of measurement.

The ratio level of measurement – Here we are the same as the interval level, with the simple addition of there being a natural zero starting point. Zero would, of course, indicate that there is none if a quantity present). At this level, ratios and differences are meaningful.

Does our height example meet this last and highest level? Does zero have meaning in terms of height? You bet your socks it does! Zero would mean there is no height, so it is meaningful.

### Here is another example for you

What would be the level of measurement for Consumer Reports which provides 3 ratings, “not recommended”, “recommended”, and “best buy”.

Since we are able to put our data in order from “best buy” to “not recommended” this satisfies the ordinal level of measurement. But since we are not able to determine a meaningful difference between all classifications of “best buy”, “recommended”, and “not recommended”. So the highest level would be the ordinal level.