Understanding the Range of a Data Set

The range measures the spread of a dataset by subtracting the minimum value from the maximum. It’s easy to calculate and provides a quick estimate of variability. However, since it only uses two values, it can be misleading if outliers are present.

Range

What is the Range of a Dataset?

The range of a data set is given by the formula: \[ \text{Range} = \text{maximum value} - \text{minimum value} \]

Advantages of the Range

Simple to Calculate: The range is easy to compute—just subtract the minimum value from the maximum value.
Quick Estimate of Data Spread: It provides a quick sense of the overall spread of the data.
Useful for Small Data Sets: For small or preliminary data sets, it can give a rough indication of variability.
Identifies Outliers Easily: A large range may indicate the presence of outliers or extreme values.

Disadvantages of the Range

Ignores Most Data Points: The range only depends on two values (maximum and minimum), ignoring all other data points.
Sensitive to Outliers: A single extreme value can drastically affect the range, making it an unreliable measure of variability.
No Information on Data Distribution: The range tells us nothing about how data is distributed between the minimum and maximum values.
Limited Use in Large Data Sets: In larger data sets, the range becomes less informative because it doesn’t reflect the overall variability accurately.

Example

Scientists are tracking the migration distances of a species of birds over several years. The distances (in miles) recorded for a sample of 10 birds are as follows:

Migration Distances
Distance (in miles)
354	400	412	375	389	410	368	390	405	392

Answer the following questions based on the data:

Part A: Find the range of the migration distances.
Part B: Explain what the range tells us about the variation in the birds' migration distances

Solution

Part A: To find the range of the migration distances, we calculate the difference between the maximum and minimum values:
- Maximum distance = 412 miles
- Minimum distance = 354 miles
Range = 412 - 354 = 58 miles
Part B: The range of 58 miles represents the spread of the migration distances among the 10 birds. A relatively small range suggests that the birds have similar migration patterns, with no extreme outliers in the distances traveled.

$$\tag*{$\blacksquare$}$$

Example

A sociologist is studying the ages of participants in a community program aimed at improving digital literacy. The ages (in years) of 12 participants are as follows:

Participants in a Community Program
Age (in years)
22	25	31	28	24	35	45	41	29	33	38	40

Ages of Participants
                            22
                            25
                            31
                            28
                            24
                            35
                            45
                            41
                            29
                            33
                            38
                            40

Use the Summary Stats Calculator to find the range of the participants’ ages.

Solution

Upload the dataset to the Summary Stats Calculator, and then click on the Minimum and Maximum checkboxes to reveal the smallest and largest values in the dataset. If you did everything correctly, the calculator should look like this:

The maximum checkbox reveals 45, and the minimum checkbox reveals 22.

Using the maximum and minimum value, we calculate the range to be \[45-22=23.\]

$$\tag*{$\blacksquare$}$$

Conclusion

The range is a simple tool for understanding data spread but lacks detail about overall variability. While useful for quick insights, it should be paired with other measures like variance or standard deviation for a more complete analysis.