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Last updated date: 23rd May 2024
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The Range

In mathematics, a range is a difference between the lowest and highest values of a numeral. In {7, 15, 4, 6, 9} the lowest value is 4, and the highest is 15, thus the range is 15 − 4 = 11. The range can also imply all the values of the output of a function. Moreover, when you start studying functions in mathematics, you'll encounter a second definition of range. To better understand range, it aids to think of functions as tiny math machines.

Range of a Function

Talking about the range of a function definition, it is the set of outputs the function accomplishes when it is pertained to its whole set of outputs. In the function machine metaphor, the range is the set of items that arise out of the machine when you insert in all the inputs.

For instance, when we apply the function notation f: R→R, we imply that f is a function →from the real numbers →to the real numbers. By this notation, we are aware that the domain (set of all inputs) of ‘f’ is the set of all possible inputs (the codomain) and as well the set of all real numbers.

But, without having to know the function f, we will be unable to identify what its outputs are further cannot even determine what its range is. All we know is that the range should be a subset of the codomain, so the range should be a subset (likely to be the whole set) of the real numbers. It is possible objects are available in the subset of codomain for which there are no inputs and for which the function will output that object.

For instance, we could describe a function f: R→R as f(x) =x2. Seeing that f(x) will invariably be non-negative, the number −3 is in the codomain set of f, but it is not in the range, since there is no input of x for which f(x) =−3. For this f, the codomain is the set of all real numbers whereas the range is the set of non-negative real numbers.

Domain and Codomain in Range

The set of values we can insert into the math machine are known as the domain (another very important concept in the range). The set of possible outcomes, once we crank those values via the math machine, is known as the ​co domain​. And the set of actual outputs or outcomes we obtain is called the range​.

Interquartile Range

The Interquartile Range also known as IQR, defines the mid ( 50%) of values when arranged from lowest to greatest in the data set. In order to determine the interquartile range (IQR), we need to ​first find the median (middle value) of the lower and upper half of the set of data. These values are assigned as quartile 1 (Q1) and quartile 3 (Q3). The IQR is thus the difference between Q3 and Q1.

Solved Examples


Think that you happen to view your math’s teacher's notebook, and you snuck the peek so far that you saw the students' grade percentages in class are {91, 84, 37, 53, 52, 88, 46, 62}. Now, you need to find out the range of this data set or we can say the range of the students' grades?


First, we need to determine the highest as well as the lowest value of the data set i.e

The highest data point = 91

The lowest data point= 37

Next, subtract the lowest value from the highest value determined:

91 - 37 = 54

Thus, the range of this specific data set is 54 percentage points.


Mr Alex drove through 8 southern states on his summer vacation. Fuel prices varied from state to state he travelled. Calculate the range of fuel prices?

Rs. 2.79, Rs. 0.61, Rs. 2.96, Rs. 3.09, Rs. 1.64, Rs. 2.25, Rs. 3.73, Rs. 1.67


Arranging the data from least to greatest, we obtain,

0.61, 1.64, 1.67, 2.25, 2.96, 2.79, 3.09, 3.73

highest - lowest = 3.73 – 0.61 = $0.48

Answer: The range of fuel prices is Rs. 3.12

Fun Facts

While finding the range, curly brackets are commonly used to enclose a set of data, so you are aware everything inside the curly brackets belongs together.

FAQs on Range

Q1. What Do We Understand by the Range in Statistics?

Answer: In Statistics, the range is nothing but simply to ask you to determine the highest and lowest values in your data set, and then find out the difference between them. Any time you run into the term "difference," it's a clear hint that you're about to subtract, thus the formula to calculate the range you'll use is: highest – lowest.

Q2. What is the Relationship Between Range and Domain?

Answer: There are a few significant relationships between range and domain that you would need to understand. First, each value in the set of domains corresponds to only one value in the range of a function. If any value(s) in the domain subset correspond to more than one value in the range, you might establish a relationship between the two sets of data, but it's not precisely categorized as a function. Nonetheless, it is possible for more than one domain value to be in correspondence to the same value in that function's range.

Q3. How to Understand the Relationship Between Range and Domain?

Answer: One of the ideal ways to understand this is to think of your very own math class. The students of a particular class represent the domain (or the details that goes into the function), while the class itself represents the function or "math machine." Your annual grades define the range, or what you achieve after cranking the constituents of the domain (students) via the function (math class).