Chapter 6 solutions - Fundamentals of Analytical Chemistry 8th ed Chapter 6 Chapter 6 6-1(a The spread or range for a set of replicate data is the

Chapter 6 solutions - Fundamentals of Analytical Chemistry...

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Fundamentals of Analytical Chemistry: 8 th ed. Chapter 6 Chapter 6 6-1 (a) The spread or range for a set of replicate data is the numerical difference between the highest and lowest value. (b) The coefficient of variation is the percent relative standard deviation or ( x s/ ) × 100%. (c) Significant figures include all the digits in a number that are known with certainty plus the first uncertain digit. (d) A Gaussian distribution or normal distribution is described by the bell-shaped curve obtained by plotting frequency versus deviation from the mean for measurements that conform to such a distribution. 6-2 (a) The sample standard deviation , s , is given by ( ) 1 1 2 - - = = N x x s N i i where x is the sample mean. The sample variance , s 2 , is given by ( ) 1 1 2 2 - - = = N x x s N i i (b) Both types of mean are obtained by summing the available replicate data and dividing by the number of data. For the population mean the number of data is large. For the sample mean the number of data are a small fraction of the population of data. (c) Accuracy represents the agreement between an experimentally measured value and the true or accepted value. Precision describes the agreement among measurements that have been performed in exactly the same way.
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Fundamentals of Analytical Chemistry: 8 th ed. Chapter 6 (d) Random errors result from uncontrolled variables in an experiment while systematic errors are those that can be ascribed to a particular cause and can usually be determined. 6-3 (a) In statistics a sample is a small set of replicate measurements. In chemistry a sample is a portion of a material that is used for analysis. (b) The sample standard deviation s is given by ( ) 1 1 2 - - = = N x x s N i i where x is the sample mean. The population standard deviation σ is given by ( ) N x N i i = - = σ 1 2 μ where μ is the population mean. 6-4 The standard error of a mean, s m , is the standard deviation of the set of data, s, divided by the square root of the number of data in the set, i.e. N s s m / = . The standard error of the mean is nearly always lower than the standard deviation of the data points in a set because N always has a value greater than 1. 6-5 Since the probability that a result lies between -1 σ and +1 σ is 0.683, the probability that a result will lie between 0 and +1 σ will be half this value or 0.342. The probability that a result will lie between +1 σ and +2 σ will be half the difference between the probability of the result being between -2 σ and +2 σ , and -1 σ and +1 σ , or ½ (0.954-0.683) = 0.135.
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Fundamentals of Analytical Chemistry: 8 th ed. Chapter 6 6-6 Since the probability that a result lies between -2 σ and +2 σ is 0.954, the probability that a result will lie outside this range is (1 - 0.954) = 0.046. The probability that a result will be more negative than -2 σ will be half this value, or 0.023.
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