![]() For the above $f$, the range is the set of non-negative real numbers while the codomain is the set of all real numbers. The set of all outputs that result from putting all inputs into the function is called the range. Since $f(x)$ will always be non-negative, the number $-3$ is in the codomain of $f$, but there is no input of $x$ for which $f(x)=-3$. For example, we could define a function $f: \R \to \R$ as $f(x)=x^2$. In 4, 6, 9, 3, 7 the lowest value is 3, and the highest. The Range (Statistics) Illustrated definition of Range (statistics): The difference between the lowest and highest values. Just because an object is in the codomain of a function, it does not necessarily mean that there is an input for which the function will output that object. Range can also mean all the output values of a function. In other words, the codomain of $f$ is the set of real numbers $\R$ (and its set of possible inputs or domain is also the set of real numbers $\R$). In the function machine metaphor, the codomain is the set of objects that might possible come out of the machine.įor example, when we use the function notation $f: \R \to \R$, we mean that $f$ is a function from the real numbers to the real numbers. If you want to know more about statistics, methodology, or research bias, make sure to check out some of our other articles with explanations and examples.The codomain of a function is the set of its possible outputs. NoteTo get a clear idea of your data’s variability, the range is best used in combination with other measures of variability like interquartile range and standard deviation. In statistics, the range is the difference between the greatest number and the least number in a set of data. It can’t tell you about the shape of the frequency distribution of values on its own. Although we have a large range, most values are actually clustered around a clear middle.īecause only two numbers are used, the range is easily influenced by outliers. In the example above, the range indicates much more variability in the data than there actually is. With an outlier, our range is now 42 years. Using the same calculation, we get a very different result this time: Range example with an outlierOne value in your data set is replaced with an outlier. One extreme value in the data will give you a completely different range. ![]() When paired with measures of central tendency, the range can tell you about the span of the distribution.īut the range can be misleading when you have outliers in your data set. The range generally gives you a good indicator of variability when you have a distribution without extreme values. Range is a concept that is used in many areas of mathematics, including algebra, calculus, and statistics. Then subtract the lowest from the highest value. In descriptive statistics, range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. ![]() Participantįirst, order the values from low to high to identify the lowest value ( L) and the highest value ( H). Range exampleYour data set is the ages of 8 participants. This process is the same regardless of whether your values are positive or negative, or whole numbers or fractions. To find it, first order the data from least to greatest.
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