Question

the speed of a new microprocessor is 800mhz but a new test of its speed gives a measurement of 820mhz. what is the abolute error? what is the relative error?​

Answer 1

Hello!

The answers are:

$AbsoluteError=20mhz$

$RelativeError=2.5(Percent)$

Why?

To solve the problem we need to remember that the absolute error is the difference between the expected value and the measured value, also, to calculate the relative error we first need to calculate the absolute error, and then, divide it by the expected measure.

So, calculating we have:

$AbsoluteError=Expected-MeasuredValue\\\\AbsoluteError=800mhz-820mhz=-20mhz$

We can see that we obtained a negative value, however, when we are working with "absolute" values, the negative symbol is discarded, so, we have that:

$AbsoluteError=20mhz$

Now, to calculate the relative error, we need to use the following formula:

$RelativeError=\frac{AbsoluteError}{ExpectedValue}*100\\\\RelativeError=\frac{20}{800}*100=0.025*100=2.5(Percent)$

So, we have that the relative error is equal to 2.5%.

Hence, we have that:

$AbsoluteError=20mhz$

$RelativeError=2.5(Percent)$

Have a nice day!