Researchers often interact with diverse data sets during their research work. Therefore, there are various methods to gain an overview of your dataset and its main characteristics, such as measures of central tendency or variance. In statistics, the range of data is fundamental to establish the difference between the highest and lowest value. The following article will cover all relevant information about this topic along with various examples.
Range of Data – In a Nutshell
The range of data is the difference between the highest and lowest value in a dataset. The greater this difference, the higher is the variability of the set.
Definition: Range of data
To determine the range of a dataset, you need to subtract the lowest value of the set from the highest one. If the range in statistics is large, the values have high variability. If the range is small, the values have minimal variability. It is counted as a measure of descriptive statistics, as it only describes how far apart the highest and lowest values are, leading to no deep analysis of the data.
Calculation
This formula helps one measure the variability of the values in a data set. For one to determine this variability, they should observe the following steps:
- Arrange all the values from a data set from the lowest to the highest.
- 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 high number does not equate to having a higher value.
Examples
- Dataset: 2,7,3,5,9 → 2,3,5,7,9 → Range: 9-2=7
- Dataset: 6,3,7,(-8),5 → (-8),3,5,6,7 → Range: 7-(-8)=7+8=15
Different types of variables
The range of data cannot be used with every type of variable. As it is determined through mathematical operations, it cannot be found with a set of nominal variables. Similarly, you also cannot use it for ordinal data, except if you use a scale of numbers (e.g., how tasty was the pizza on a scale of 1-5?), but this is not useful as the range is actually determined beforehand.
Only with quantitative data, the statistical range is truly helpful to determine the variability of a dataset.
Examples
- As part of a survey, you ask participants to name their age (discrete variable), resulting in the following distribution:
22,24,35,43,25,32,42,36,28,31 → 22,24,25,28,31,32,35,36,42,43
43-22=21 - For the next question, you ask about their weight (continuous variable):
90.9 kg, 58.8 kg, 49.2 kg, 75.5 kg, 67.1 kg, 95.3 kg, 80.3 kg, 62.4 kg, 85.6 kg, 51.7 kg
→ 49.2 kg, 51.7 kg, 58.8 kg, 62.4 kg, 67.1 kg, 75.5 kg, 80.3 kg, 85.6 kg, 90.9 kg, 95.3 kg
95.3 kg – 49.2 kg= 46.1 kg
Use and Importance
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. It is often the first characteristic of a dataset to determine, since it is easy to see and can give you a first overview of the dispersion of the values.
Outlier effect
An outlier refers to a data value that is abnormally distant from the other values. While a statistical range of data is a good and effective way to determine the spread of the values within a data set, it is also highly affected by outliers. In these cases, the entire range may not be an accurate indication of values’ variability. This inaccuracy is because one extreme value alters the range completely.
Examples
- Dataset: 2,5,3,8,5,9,11,15,7,76 → 2,3,5,5,7,8,9,11,15,76 → Range: 76-2=74
- Without the outlier of 76, the range would be 15-2=13, which is way more accurate and realistic.
The interquartile range
Do not confuse the statistical range of data with the interquartile range. The interquartile range calculates the middle 50% of the dataset. This measure is less sensitive towards outliers and thus often used with widely dispersed values. It is calculated by using quartiles and quantiles, looking for the difference between the first and third quartile. A quantile is a section of the data, where the given percentage of values lie below. Quantiles are calculated with the formula 
, where n is the number of values in your set and p is the percentage of the quantile.
Example
The 30% Quantile is written as and describes the point in the dataset, where 30% of the values are lower than this point. In an exemplary dataset with 10 values from 1-10, 3 would be the 30% Quantile.
Quartiles are 25% steps of quantiles, meaning there is the first or lower quartile (25%), the second quartile (50%; also called the median), and the third or upper quartile (75%).
Example
If we now take the dataset from before (1-10), we need to keep in mind that when calculating quantiles, we always need to adjust decimals upwards. Meaning our first quantile will be 10×0.25=2.5 so it will be 3. The third quartile is 10×0.75=7.5, so 8. That results in an interquartile range of 8-3=5.
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FAQs
One finds the statistical range of a data set by subtracting the minimum value of the dataset from its maximum value.
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.
Yes. The statistical range of data applies to any type of values in a data set, including fractions.
Outliers have a profound effect on the range, since they can skew this measure greatly. If your dataset is suspected to have outliers or widely dispersed values, you should rather determine the interquartile range.
