# Uncertainties ## Random Error

### In order to calculate the Random Error value, the following formula can be used :- ## Example 1 -

### The below data was gathered from an Ohm's Law experiment. Calculate the average value of the Resistance and the Error in that reading :- ## Systematic Error

### A Systematic Error is very different from a Random Error. Unlike Random, all measurements effected by a Systematic Error are affected in same way, all are either too large or too small. If magnitude of this Error can be found numerically, each data point in the results can be corrected accordingly. An example of this is shown in the diagram below :- ### This is due to the issue of rounding to the nearest unit. Both meters below show Voltage readings; Analogue on left and Digital on right. Both have the same minimum marked unit of 1 Volt. ## Uncertainty in a Sum or Difference Equation

### When a calculation requires addition or subtraction, the absolute error in the final value can be calculated using the following formula :- ## Uncertainty in a Product or Quotient Equation

### When a calculation requires multiplication or division, the absolute error in the final value can be calculated using the following formula :- ## Example 2 - ## Example 3 - ## Example 4 -

### In an experiment, the Current through a fixed Resistor was measured and the following data was collected :- ## Uncertainty Calculations - LINEST Function

### To calculate this, the starting point required is the same as for a graph :- ### To allow the calculation of a LINEST function, an additional 4x4 cell section needs to be used. The following shows the additional layout, as well as labels for each :- ### Once this calculation has been typed into the first cell, press Ctrl+shift+Enter, and the table should now show four values :- ### As was stated earlier, the gradient of this graph shows 1/Resistance. If the axes are reversed (Current X axis, Voltage Y axis), the gradient will then give resistance, as shown below :- 