>Dispersion>What Does Range in Statistics Mean?

What Does Range in Statistics Mean?

In this entry, you will learn about the range of data. The range expresses the spread of values in a data set—that is, the difference between the highest and the lowest value in the set.

Example 1

The students in 9^th grade at Westview Junior High School received the following grades on a math test:

$\begin{array}{l} 4, 4, 1, 1, 2, 0, 3, 2, 3, \\ 2, 3, 0, 0, 2, 0, 4, 3, 1, 2 \end{array}$

$4, 4, 1, 1, 2, 0, 3, 2, 3, 2, 3, 0, 0, 2, 0, 4, 3, 1, 2$

What is the data set, and what is the range of the data?

The data set is all the grades you see above—the collection of all the data put together. The data here are the grades the students got on the math test.

The range is the difference between the highest grade and the lowest grade—that is, the spread in the data set. The range is therefore $4 - 0 = 4$ .

Theory

The range is the difference between the highest and the lowest value in a data set. The range is called a measure of dispersion because it provides an interpretation of the spread of the values in the data set.

Example 2

Ten students at Eastview Junior High School were asked how many hours they watched Netflix each day. You can see the results here:
$4, 0, 10, 2, 4, 1, 4, 8, 3, 2$

What is the range, and what can you interpret from it?

The range is the difference between the highest and the lowest value, that is, $10 - 0 = 10$ . From this you can interpret that there are very big differences in the number of hours the students at Eastview Junior High School watch Netflix. In other words, there is a large spread in the data set.

Example 3

The following temperatures were measured on a December day. What is the range of temperatures? $\begin{matrix} - 5 \circC, - 3 \circC, - 3 \circC, 0 \circC, 1 \circC, \\ 3 \circC, 2 \circC, - 2 \circC, - 4 \circC \end{matrix}$

The range is $3 - (- 5) = 8$ . From this you can interpret that the temperature varied by $8$ ∘C on this December day.

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Interquartile Range and Semi-interquartile Range

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