Question

You estimate that the driving distance from Raleigh, NC to Charlotte, NC is around 180 miles. When you looked it up on the internet, you found that the actual distance is only 167.5 miles. What was the relative (percent) error of your estimate? In other words, how far off were you from the actual value?

Answer 1

i. The relative error in the estimated distance is approximately 7.5%.

ii. The value of the estimated distance was about 12.5 miles far of from the actual value.

Explanation:

Given that;

Estimated distance ≅ 180 miles

Actual distance = 167.5 miles

Then,

Estimated distance - Actual distance = 180 - 167.5

= 12.5 miles

So that,

Relative error =
`((estimated distance - actual distance)/(actual distance) )` × 100%

=
`(12.5)/(167.5)` × 100%

= 0.07463 × 100%

= 7.5%

i. The relative error in the estimated distance is approximately 7.5%.

ii. The value of the estimated distance was about 12.5 miles far of from the actual value.