Statistics

Statistics

Let us look at one more example:

28, 30, 31, 33, 35, 36, 37, 42

In this example, there are no repeating ages. Therefore, this data set does not have a mode. A data set can only have a mode when repeating numbers are observed.

*Tip: A data set can have 1 mode, more than 1 mode, or no modes!

Range : The range is the interval between the lowest and highest values, of a given number set place in numerical order. The range can give us useful information about a given population or data set.

Let’s look at our original data set:

Student ages: 31, 33, 30, 31, 35, 33, 36, 28, 42, 37, 33

The 1st step is to order the data set, just like we did previously. This allows you to better visualize and identify the lowest and highest values.

Our ordered data set is: 28, 30, 31, 31, 33, 33, 33, 35, 36, 37, 42

From the above example, we can identify the lowest or youngest age is 28 and the highest, or oldest age, is 42. Therefore, we would say that our population range is 28 years to 42 years. The rest of the class ages fall between 28 and 42 years.

But what if we have the following age of students?

Student ages: 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28

Now all 11 students are 28 years old; therefore, we do not have a range in this given population example.

Let us look at another example of student ages for a given class:

Student ages: 20, 21, 22, 22, 23, 24, 24, 59

We identify the lowest or youngest age to be 20 and the highest or oldest age to be 59. Therefore, our class age range is 20 to 59 years. This appears to give us a large range in student ages. However, we can clearly see that the majority of the students are in their early twenties, with a single student being 59 year old. In this case, the range alone does not yield a true representation of the population. We can say that the range is skewed due to an outlier, the 59 year old student. We will discuss outliers latter on in the text, but keep this concept in mind as you progress to data interpretation. *Questions to think about: Why is it important to study the range of a population? What useful information can the range give use about a given population? How can the results skew the actual population sample?

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