# Properties and Uses of Range in Statistics

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The range is the simplest quantity that can be used to measure the degree of dispersion/spread in the given data values. It is defined as the difference between the largest and the smallest value in the given set of data. In this article, we list some of the important properties and uses of range in statistics.

### Properties of Range:

1. The value of range is always non-negative. Since finding the range involves subtracting a smaller number from a larger number we see that range is always either or positive or equal to zero.
2. The value of the range is equal to zero if and only if the given set of data values are all equal to each other. For example, the range of the below set of 6 data values 3, 3, 3, 3, 3, 3 is equal to zero because the highest and the lowest values are both equal to 3.
3. If the range is non-zero we can conclude that the given data values are not all equal to each other.
4. For a continuous frequency distribution we can find the range by subtracting the lower limit of the smallest class from the upper limit of the highest class.
5. When finding the range for a frequency distribution we do not consider the frequencies of the classes. This is because the range is calculated only on the basis of the two extreme observations.
6. The value of the range is independent of the change in origin. This means that the range remains unchanged if we add the same number to all the data values. For example consider the following set of data values: 3, 4, 7, 9, 11, 13. We have that, Range = 13 – 3 = 10. Now if we change the data values by adding 2 to each number we get, 5, 6, 9, 11, 13, 15. Notice that the range = 15 – 5 = 10 still remains unchanged.
7. The value of range is dependent on change in scale. If we multiply all data values by a number “A” then the value of the range is also multiplied by “A”. For example consider the following set of data values: 1, 2, 4, 5, 7, 9. Here Range = 8. Now if we multiply all the data values by “A=3” we get, 3, 6, 12, 15, 21, 27. The range of the above set of data is equal to 3*8 = 24.
8. The value of range is not based on the entire set of observations but only on the two extreme observations. This makes the range an unreliable measure of dispersion.

### Uses of Range:

1. Range can be used to measure variation in variable where the data does not fluctuate too wildly. Thus range can be used in fields such as stock markets, interest rates, etc.
2. Range is very useful in our day to day life. For example, when we formulate a budget for buying clothes we first set an acceptable lower and upper limit for our budget. We then spend the money in the acceptable range.
3. Range is used in weather departments when making annoucements of daily temperature to the public. The department releases a range of values within which the temperature may lie.
4. Range is used as a measure of dispersion in the field of statistical quality control.

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