How to Find Range?
In statistics, the range is the size of the smallest interval which contains all the data. It provides an indication of statistical dispersion. It is always measured in the same units as the data. As it only depends on two of the observations, the range is useful for showing the spread within a dataset and. And also for comparing the spread between similar datasets. Let us discuss the methods for how to find range.
Definition of Range
In statistics, the range is the difference between the maximum and minimum values of a data set. It serves as one of two important features of a data set. The simple formula for a range is the difference of maximum and minimum values in the dataset. Also, it provides statisticians with a better understanding of how varied the data set is.
In addition, two main features of data sets are the center of the data and the spread of the data. Furthermore, the center of data can be measured in a various number of ways. Also, some popular of these are the mean, median, mode, and midrange.
Limitations of Range
The range is a very crude and fundamental measurement of the spread of data because it is very sensitive to outliers. Thus, as a result, there are certain limitations to the utility of a true range of a data set for statisticians. This is because a single data value can greatly affect the value of the range.
Applications of Range
- The range is an easy but good way to get a basic understanding of the spread of the numbers in the data set. Moreover, it is easy to calculate as it only requires a basic arithmetic operation.
- The range can also be used to estimate another measure of spread which is the standard deviation. Also, we can use a simple method to find the standard deviation by using what we call the range rule.
- The range also occurs in a boxplot and whiskers plot. In this, the maximum and minimum values are both graphed at the end of the whiskers of the graph. The total length of the whiskers and box is equal to the range.
Method of How to Find Range?
The calculation of the range is very straightforward. In addition, we simply we need to find the difference between the largest data value in our set and the smallest data value.
Stated as Range = Maximum Value–Minimum Value.
E.g., in the data set 4,6,10, 15, 18 has a maximum of 18, a minimum of 4 and a range of 18-4 = 14.
Hence we have to arrange the set of numbers from smallest to largest and to subtract the smallest value from the largest. So, the steps are as follows:
Step-1: Arrange the set of numbers in order from smallest to largest.
Step-2: Identify the smallest and largest numbers in the set, which will be at first and last position.
Step-3: Subtract the smallest number from the largest.
Step-4: Write down your range.
Example of Range
The Sharma family drove through 6 North India states on their summer vacation. CNG prices varied from state to state. What is the range of LPG prices?
Rs. 79, Rs .71, Rs. 96, Rs. 92, Rs. 84, Rs. 75
Solution: First do the ordering the data from smallest to greatest, we get:
Rs. 71 , Rs. 75 ,Rs. 79 ,Rs. 84 ,Rs. 92 , Rs. 96
highest – lowest = Rs. 96 – Rs. 71 = Rs. 25
Thus the range of LPG prices is Rs. 25
Solved Question for You
Q.1.How to find range of a function?
Ans: we can define the range of a function, as the set of all possible values which it can produce. Thus no matter what value we give to x, the function is always positive. If x is 2, then the function returns x as squared value i.e. 4.