Percentage error can be defined as the discrepancy between one observed and a true or accepted value. The result often varies when data is being measured from the true value, and this is the percentage error. 

There are so many possible reasons for the occurrence of percentage error, and one of the many reasons is human error. Another possible reason for the occurrence of percentage error is due to a technical flaw in the device which is being used for calculations and measurements. 

No matter what the reason of percentage error is, we need to calculate it. The computation of percentage error does involve the use of absolute error. An absolute error is simply the difference between an observed and a true value. Once we get the absolute error, it gets divided by the true value to get a relative error.

The relative error is multiplied by 100 to obtain our percentage error. Here is an equation for clarification:

Absolute error = |Vtrue - Vobserved|

In these equations, we assume that the true values are known. In most of the cases, true values are unknown. When true values are unknown, we use standard deviation to represent the error. 

Key points in order to understand the Percent Error

• The basic purpose of finding a percent error is to know and gauge how close the measured value is to a true value. 
• In so many fields, a positive number is used to express percent errors. While in others, percent errors can be expressed by a positive or a negative number. Positive or negative signs always kept determining either the measured or recorded values are falling above or below the expected value. 
• One type of error calculation is the percent error. There are two other types of errors, which are absolute error and relative error. Percent error is an integral part of comprehensive error analysis. 
• Percent error is calculated to know whether there is a need to drop the sign or not on the calculation and to report the values using exact and correct numbers of significant figures. 

Summation

There is always a need for the addition of many variables in almost all the mathematical equations. Summation, which is also known as sigma notation, is a simple shorthand that is used to compact expressions for a sum of the values of a variable. 

Let us understand this with the help of an example. Let x1, x2, x3, …xn denote a set of n numbers. x1 is the first number in the set. xi represents the ith number in the set.

In order to find a summation, it is always suggested to use a summation notation calculator to get reliable and flawless results. 

Summation notation involves?

• It involves a summation sign
• It is denoted by a symbol S. S is a Greek upper-case letter, S. This sign gives an indication that there is a need to sum the elements of a sequence. Elements of the sequence that are required to be summed appear to the right of the summation sign. 
• The variable of summation is the variable that is being summed. It is often represented by an index that is placed beneath the summation sign. We use i to represent the index. The index is also represented with the help of j and t in some of the cases. 
• The index appears that the expression i = 1. The index always assumes that the values are starting on the right-hand side of the equation and ending with the value above the summation sign. 
• The starting point for the summation that can be called as the lower limit of the summation
• The stopping point for the summation that can be called as the upper limit of the summation