Pipettes are used when measuring the volumes of liquids with high degree of precision. The following volumes were obtained during the calibration of a 10.00 mL pipette: 10.15 mL, 9.95 mL, 9.99 mL, and 10.02 mL. Calculate the standard deviation for these measurements.

Question

Lena Wall

Chemistry

31 October, 05:03

Pipettes are used when measuring the volumes of liquids with high degree of precision. The following volumes were obtained during the calibration of a 10.00 mL pipette: 10.15 mL, 9.95 mL, 9.99 mL, and 10.02 mL. Calculate the standard deviation for these measurements.

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Bentley Conrad · Answer 1

0.075

Explanation:

First obtain the mean of the measurement;

Mean = 10.15 + 9.95 + 9.99 + 10.02/4 = 10.03

Then obtain d^2 = (mean-score) ^2 for each score;

(10.15-10.03) ^2 = 0.0144

(9.95-10.03) ^2 = 0.0064

(9.99-10.03) ^2 = 0.0016

(10.02-10.03) ^2 = 0.0001

∑d^2 = 0.0144 + 0.0064 + 0.0016 + 0.0001

∑d^2 = 0.0225

Variance = ∑d^2/N = 0.0225/4 = 0.005625

Standard deviation = √0.005625

Standard deviation = 0.075