Range

The range of a collection of numbers is the difference between the highest & lowest values. Subtract the lowest from the highest number in the distribution to discover it.

A set of output values produced by a function is referred to as a function’s range. It is the difference between the highest and lowest values in a set (statistics). A collection of real numbers that includes all numbers between any two numbers in the set (mathematics), also known as a range.

Column space, often known as a matrix’s range, is the set of all possible linear combinations of the matrix’s column vectors. In projective geometry, a projective range is a line or a conic. In logic, a quantifier’s range.

Range meaning

The difference between the largest and smallest values in a set of data is known as the range in statistics. The distinction is that a collection’s range is calculated by subtracting the sample maximum and minimum values. Range, on the other hand, has a more complicated definition in descriptive statistics.

In a frequency distribution, range is the difference between the highest and lowest observation. For all sorts of series, the formula is nearly the same.

• Individual Series: Subtract the lowest observation from the highest observation in each individual series.
• Discrete Series: Individual Series and Discrete Series are the same thing. Take the lowest observation and subtract it from the greatest. It makes no difference what frequency you use.
• Continuous Series: Range is computed by subtracting the upper limit of the highest class interval from the lower limit of the lowest class interval in a continuous series.

Range in statistics formula

The range formula calculates the difference between a collection of numbers’ highest and lowest values. The range formula is often used in variability and is usually utilised in statistics where the range is the spread of figures or data from the lowest to the highest value.

A measure of dispersion that highlights how varied the numbers are, and it can be calculated using a simple formula.

By calculating the difference between the lowest and highest numbers, the formula aids in establishing the set’s centre. The larger the range of a distribution, the higher the variability, and the smaller the range, the lower the variability. Other parts of statistics, such as mean, median, and mode, are included in the range formula. As a result, the formula for calculating the range is as follows:

R= H-L

Where,

R stands for range.

H stand the highest value 

L is the smallest number

Range Formula: How to Use It

There are two main stages to take in order to compute the range using the range formula:

• Place all of the numbers in the data collection from lowest to highest value. 
• Subtract the lowest value from the highest value in the data set using the range formula.

These procedures can be applied to any number, including whole numbers and fractions. If the numbers in the data set are positive or negative, the range formula can be employed.

Advantages 

When you have a distribution without extreme values, the range is often a useful indicator of variability. The range, when used in conjunction with measurements of central tendency, can reveal the distribution’s spread. However, if your data collection contains outliers, the range can be deceiving. You’ll get a whole different range if you take one extreme value out of the data.

Example of range

Example: 1 What is the range of possibilities for the following observation 1, 2, 4,6,8,10,14?

Solutions: The difference between the highest and lowest observation is known as range. The range is 14 since the greatest observation is 14 and the lowest observation is 11.

14-1=13

Example: 2 In the numbers 8, 11, 5, 9, 7, 6, 3616

Solutions:  5 is the lowest value 

                    while 3616 is the highest.

As a result, the range is   3616 – 5 = 3611

Conclusion

In this article, we are study that the range of a collection of numbers is the difference between the highest and lowest values. Subtract the lowest from the highest number in the distribution to discover it. The range is a simple yet effective technique to acquire a basic idea of the data set’s numerical distribution. Furthermore, it is simple to calculate because only a basic arithmetic operation is required. The range can also be used to calculate the standard deviation, which is another measure of spread.