Question

An object was carefully weighed five times on a multiple-beam balance. The balance was zeroed each time. The masses were: 11.36 g 11.37 g 11.40 g 11.38 g and 11.39 g

a. Calculate the average value of these measurements. (Show all work.)

b. Calculate the standard deviation, s.d., of this set of measurements using the range of the data and the squareroot of the number of measurements averaged. (Show all work.)

Answer 1

Answer:

11.38 g

0.014142

Step-by-step explanation:

part a

Mean = Sum of all results / No. of results

Mean = (11.36 + 11.37 + 11.40 + 11.38 + 11.39) / 5

Mean = 11.38 g = E (X)

part b

Var (X) = E (X^2) - (E(X))^2

S.d = sqrt (Var (X))

Compute E (X^2):

E (X^2) = (11.36^2 + 11.37^2 + 11.40^2 + 11.38^2 + 11.39^2) / 5

E (X^2) = 129.5046

(E(X))^2 = 11.38^2 = 129.5044

Var (X) = 129.5046 - 129.5044 = 0.0002

s.d = sqrt (0.0002) = 0.014142