What is the difference between absolute error and relative error?

Absolute Error

Difference between measured and true value.

Relative Error

Ratio of absolute error to true value.

What is the formula for calculating mean absolute error?

Where:

x_i = individual measurements

x_mean = mean (true) value

n = number of observations

What is the formula for relative error?

Ratio of absolute error to the true (or mean) value.

What is the arithmetic mean of measurements a₁, a₂, ..., aₙ?

Mean = (a₁ + a₂ + ... + aₙ) / n

Velocity v = At² + B/t. Dimensions of A & B?

A → [L T⁻³], B → [L].

True/False

Relative error in subtraction is always greater than in addition.

True (small differences magnify error).

A sphere’s radius = 2.00 cm with error 0.01 cm. Find percentage error in surface area & volume.

Surface area error = 2Δr/r = 1%, 

Volume error = 3Δr/r = 1.5%.

True/False

If the measured value of acceleration = 9.8 m/s², then order of magnitude is 9.8.

False

 (Order of magnitude = 10⁰ = 1)

Fill in the Blank

The unit of permittivity ε₀ is ____.

A screw gauge has pitch 1 mm and 200 divisions. What is its least count?

Which physical quantity has dimensional formula [M⁰ L⁰ T⁰]?
a) Strain
b) Angle
c) Specific gravity
d) All of these