The range is one of the terms that is used very often in math. Besides, it is also one of the easiest ones to understand.
Simply put, the range is only the difference between the highest value and the lowest value within any set of numbers.
Let’s say that you have the following set of numbers:
34 47 45 42 37 35 40
In order to determine the range, the only thing you need to do is to determine the difference between the highest number of the set to the lowest number of the set.
So, the range in this case is:
Range = 47 – 34 = 13
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While the range seems pretty obvious and easy to calculate, please notice that the set of numbers we gave as an example are very close to each other.
So, let’s now assume that you have a different set of numbers for which you need to discover the range:
8, 11, 5, 9, 7, 6, 3616
As you can see, the highest value in this set is 3616 and the lowest value in this same set is 5. Even though according to the rules, you would need to find the difference between these two numbers to determine the range, you wouldn’t get a precise range. After all, all the numbers in the set with the exception of the 3616 are all near 10. So, having a range of 3611 (3616 – 5) doesn’t really make a lot of sense.
So, what can you do?
Whenever you have a specific set of numbers that either has extremely low values or extremely high values, you should prefer to use the standard deviation.
How Can You Use The Standard Deviation?
When you have a set of numbers that include extremely high values or extremely low values, you should calculate the standard deviation instead of the range.
Here is how you can easily do it.
Let’s say that you have the following set of values: 3 9 6 10 145
As you can see, the 145 is an extremely high value compared to al the others. So, in this case, you need to calculate the standard deviation instead of the range.
1. Determine the mean of the set of values:
In order to determine the mean, you will need to add them all and then divide the result by the total number of values that are included in the set.
According to our example, we have 5 values. So:
Mean = (3 + 6 + 9 + 10 + 145) / 5 = 34.6
You can also use our Range calculator to help you with your calculations.
2. You will now need to subtract each number from the mean:
According to our example, you will need to do the folowing calculations:
3 – 34.6 = – 31.6
6 – 34.6 = -28.6
9 – 34.6 = -25.6
10 – 34.6 = -24.6
145 – 34.6 = 110.4
3. You will now need to find the squared result for each one of the numbers you got:
(-31.6)^2 = 998.56
(-28.6)^2 = 817.96
(-25.6)^2 = 655.36
(-24.6)^2 = 605.16
110.4^2 = 12188.16
Summing up all the squares: 15265.2
Now, you need to divide the sum of all squares by (n-1):
15265.2 / (5 – 1) = 3816.3
So, you just have the variation of your set of numbers: 3816.3.
When you just need to make simple calculations, make sure to use our free calculator.
4. Finally, calculate the standard deviation:
In order to calculate the standard deviation, you just need to take the square root of the variance:
Standard Deviation = √3816.3 = 61.776
As you can see, this number makes a lot more sense than simply determining the range.