Chapter 1, Problem 67RIL

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# A general chemistry class carried out an experiment to determine the percentage (by mass) of acetic acid in vinegar. Ten students reported the follow­ing values: 5.22%, 5.28%, 5.22%, 5.30%, 5.19%, 5.23%, 5.33%, 5.26%, 5.15%, 5.22%. Determine the average value and the standard deviation from these data. How many of these results fell within one standard deviation of this average value?

Interpretation Introduction

Interpretation:

The average value and the standard deviation has to be determined and the number of values that fall within one standard deviation of the average value has to be given.

Concept Introduction:

Standard Deviation: A series of measurements is equal to the square root of the sum of the squares of the deviations for each measurement from the average, divided by one less than the number of measurements.

SD=|xμ|2Nwhere,xis values in the data set,           μisaverage of the data set (mean value),            N is no.of data points.

Explanation

The average value and the standard deviation is calculated as,

â€‚Â SD=âˆ‘|xâˆ’Î¼|2Nwhere,â€‰xâ€‰isÂ valuesÂ inÂ theÂ dataÂ set,Â Â Â Â Â Â Â Â Â Â Â Î¼â€‰isâ€‰averageÂ ofÂ theÂ dataÂ setÂ (meanÂ value),Â Â Â Â Â Â Â Â Â Â Â Â NÂ isÂ no.ofÂ dataÂ points.GivenÂ :Â xÂ =Â 5.22%,5.28%,5.22%,5.30%,5.19%,Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 5.23%,5.33%,5.26%,5.15%,5.22%.FindÂ meanÂ valueÂ (Î¼):Î¼=5.22%+5.28%+5.22%+5.30%+5.19%+5.23%+5.33%+5.26%+5.15%+5.22%10Â Â Â =Â 5.24Â %DeterminationMeasuredÂ valuesDifferenceâ€‰betweenâ€‰Measurementâ€‰andâ€‰Averageâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰(xâˆ’Î¼)SquareÂ ofÂ Differenceâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰|xâˆ’Î¼|215.22%âˆ’0.024Ã—10âˆ’425.28%0.041.6Ã—10âˆ’335.22%âˆ’0.024Ã—10âˆ’445

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