Question

A student obtains the following values for the mass of three pennies: 1.2425 g, 1.1992 g, and 1.1223 g

Part A - Calculate the average mass of the three penniea

Part B - Calculate the average deviation

Part C - Calculate the standard deviation

Part D - Calculate the relative percent deviation

Answer 1

Part A :

Average x' = sum of all masses of pennies / total num of pennies

x' = 1.2425 +1.992 + 1.1223 / 3

= 3.564 / 3 = 1.188

Part B:

Average deviation = | x₁ - x'| + | x_{2 -} x' | + | x₃ - x' | / 3  

= |1.2425 - 1.88| + | 1.1992 - 1.88| + |1.1223 - 1.88| / 3

= 0.0545 + 0.0112 + 0.0657 / 3 = 0.0438

Part C

Standard deviation

S = square root ( x₁ - x' )² + ( x₂ - x')^2 + ( x₃- x') ^2 / n-1

S = 0.0608776642

Part D

RSD = 100 S / x' = 100 × 0.608776642 / 1.188 = 5.12 %