Question

4.5s

4.6s

4.7s

4.5s

4.4s

4.4s

4.6s

4.5s

Question 1). Calculate the percent error.

Question 2). If the standard value is 4.12s, what is the percent difference?

Answer 1

1)

First you calculate the average of all 9 values.

Then find the difference between each value and the average, giving you 8 deviations.

Now you find the average deviation, but don't just add them together and divide by 8, you'll get zero! Give it a try and see for yourself.

Instead you must convert all 8 deviations to positive numbers before you average them. There are two ways of doing this: one is called the Average Deviation and the other is called the Standard Deviation. Choose just one method:

A. Average Deviation: Just convert the negative deviations to positive by ignoring the minus sign. This is called taking the "absolute value" of each number. Now add them up and divide by 9.

B. Standard Deviation: Calculate the square of each deviation (to make them all positive), add them up and divide by 9. Now take the square-root of the average. You take the square-root because squaring the deviations makes them much larger (or smaller) than they really are.

Finally, convert to a percent error by dividing your Average Deviation or Standard Deviation by the average of the measurements and multiplying by 100.

using 1st method

average = 4.525

deviations are : 0.025 , - 0.075 , -1.075 ,0.025 , 1.025 ,1.025 , -0.075 , 0.025

Average deviation = 0.41875

percent error = average deviation/ average *100 = 0.41875/4.525 *100 = 9.25414 %

b)

Calculate percentage difference
between V₁ = 4.525 and V₂ = 4.12

( | V₁ - V₂ | / ((V₁ + V₂)/2) ) * 100

= ( | 4.525 - 4.12 | / ((4.525 + 4.12)/2) ) * 100
= ( | 0.405 | / (8.645/2) ) * 100
= ( 0.405 / 4.3225 ) * 100
= 0.093696 * 100

= 9.3696% difference