Chemistry and Chemical Reactivity (9th Edition)

Published by Cengage Learning
ISBN 10: 1133949649
ISBN 13: 978-1-13394-964-0

Let's Review: The Tools of Quantitative Chemistry - 2 Making Measurements: Precision, Accuracy, Experimental Error, and Standard Deviation - Review & Check for Section 2 - Page 31: 1



Work Step by Step

From the definition of standard deviation: $\sigma = \sqrt{\dfrac{\sum (x_i-\bar{x})^2}{n-1}}$ Given the values: $n=4; \bar{x} = \dfrac{8.19+8.22+8.21+8.25}4=8.2175\ g$ Plug this into the standard deviation formula: $\sigma = \sqrt{\dfrac{(-0.0275)^2+(0.0025)^2+(-0.0075)^2+(0.0325)^2}3}$ $\sigma=0.025\ g$ With the rounding half to even rule it's 0.02 g.
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