# Statistical Range of Data — Tutorial with Example

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Researchers often interact with diverse data sets during their research work. In statistics, the statistical range of data is fundamental to establish the difference between the highest and lowest value.

## Statistical Range of Data – In a Nutshell

• Statistical range of data gives the researcher a clear image of the spread of the whole dataset.
• Statistical range of data illustrates the possibility of extreme values in a given data set.
• Statistical range of data is significant to demonstrate variability.
• Large statistical range of data depicts large variability.
• Small statistical range of data depicts minimal variability.

## Definition: Statistical range of data

Statistical range of data refers to the variation between the largest value and minimum value within a data set.1

One can calculate the statistical range of data by subtracting the minimum value from the maximum value. If the range is large, the values have high variability. If the range is small, the values have minimal variability.

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## Calculating the statistical range of data

The formula applied in calculating the range is:

represents range

stands for the maximum value in a data set

represents the lowest value in a data set

This formula helps one measure the variability of the values in a data set.2 For one to determine this variability, they should observe the following steps:

1. Arrange all the values from a data set from the lowest to the highest.
2. Subtract the minimum value from the maximum value.

These steps apply to all forms of values, including fractions, negative values, positive values, and whole numbers. One has to be cautious when dealing with negative values as a value with a big number does not equate to having a bigger value.

Example Calculation

In this calculation, the data set will include ten values.

 Participant 1 3 3 4 5 6 7 8 9 10 Age 30 58 49 46 44 37 67 38 57 29

The first step is to arrange these values in order from the lowest to the highest:

 Age 29 30 37 38 44 46 57 49 58 67

The second step is to apply the formula:

In this case,

• the highest value is 67
• The lowest value is 29

67-29= 38

Therefore, the statistical range of data in this example is 38 years.

## What can the statistical range of data tell you?

A statistical range of data is an essential measure of variability in a data set that does not have extreme values. This range when combined with units of central tendency can help a researcher establish the span of distribution.

## The statistical range of data with outliers

While a statistical range of data is a good and effective way to determine the spread of the values within a data set, it can sometimes have outliers. An outlier refers to a data value that is abnormally distant from the other values.3

In the case of outliers, the range may not be an accurate indication of values’ spread/ variability. This inaccuracy is because one extreme value alters the range completely.

Using the example above with an outlier in place of one of the values:

 Participant 1 2 3 4 5 6 7 8 9 10 Age 130 58 49 46 44 37 67 38 57 29

Our example:

In the new data set,

After including an outlier, the new range is now 101.

The new data set with an outlier has a significantly higher range, which signifies more variability than exists among these values. This large range is not an accurate representation as most of the values are closer to the middle value.

The statistical range of data only uses two values to determine variability. As such, the variability can be influenced by outliers. One cannot rely on this individual method to determine the values’ frequency of distribution.

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## FAQs

#### How do you find the statistical range of a dataset?

One finds the statistical range of a data set by subtracting the minimum value of the dataset from its maximum value.

#### How can you define a range of statistics?

A range refers to the difference in variation between the biggest value and smallest value in a data set. The range is the simplest tool adapted to determine variability.

#### Does the statistical range of data apply to fractions?

Yes. The statistical range of data applies to any type of values in a data set, including fractions.

#### What methods can one use to find outliers in a data set?

One can easily find outliers by sorting the values from the lowest to the highest values. If there’s an abnormal difference between these values, there is an outlier.

Other methods of finding outliers include interquartile range and other statistical procedures.

## Sources

1 Zulfigar, Ali. Bhaskar, S Bala. “Basic Statistical Tools in Research and Data Analysis.” Indian Journal of Anaesthesia. September, 2016. https://journals.lww.com/ijaweb/Fulltext/2016/60090/Basic_statistical_tools_in_research_and_data.10.aspx.

2 Study.com. “Range of Data.” July 25, 2022. https://study.com/learn/lesson/range-of-a-data-set.html.

3 Whitley, Elisa. Ball, Jonathan. “Statistics Review 1: Presenting and Summarising Data.” BMC. November 29, 2001. https://ccforum.biomedcentral.com/articles/10.1186/cc1455.

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