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Sep 12, 2021 · The standard deviation, s, describes the spread of individual values about their mean, and is given as \[s = \sqrt{\frac {\sum_{i = 1}^{n} (X_i - \overline{X})^{2}} {n - 1}} \label{4.1}\] where \(X_i\) is one of the n individual values in the data set, and \(\overline{X}\) is the data set's mean value.
Sep 12, 2021 · (a) What are the mean and the standard deviation for the number of 13 C atoms in a molecule of cholesterol (C 27 H 44 O)? (b) What is the probability that a molecule of cholesterol has no atoms of 13 C? Solution
The standard deviation, \(\sigma\), describes the spread of a data set’s individual values about its mean, and is given as \[ \sigma=\sqrt{\frac{\sum_{i}^{ }(X_i-\overline{X})^2}{n-1}} \tag{4.1}\] where X i is one of n individual values in the data set, and X is the data set’s mean (average) value.
- 2.1 Aim of Statistics in Analytical Chemistry
- One of the values is quite different from the others; can I simply ignore it?
- 2.2 Mean, Variance, & Standard Deviation
- Mean:
- Variance:
- Standard Deviation:
- C =102.1 ± 4.7 mg (mean ± s, n = 5)
- Random errors:
Modern analytical chemistry is concerned with the detection, identification, and measurement of the chemical composition of unknown substances using existing instrumental techniques, and the development or application of new techniques and instruments. It is a quantitative science, meaning that the desired result is almost always numeric. We need t...
This depends on the range of the values you obtained, how different the suspect value is from all the others, and how close the remaining results are to one another. Use either Dixon's Q test or Grubb's test on the data.
The three main measures in quantitative statistics are the mean, variance and standard deviation. These measures form the basis of any statistical analysis.
Technically, the mean (denoted μ), can be viewed as the most common value (the outcome) you would expect from a measurement (the event) performed repeatedly. It has the same units as each individual measurement value.
The variance (denoted 2) represents the spread (the dispersion) of the repeated measurements either side of the mean. As the notation implies, the units of the variance are the square of the units of the mean value. The greater the variance, the greater the probability that any given measurement will have a value noticeably different from the mean.
The standard deviation (denoted ) also provides a measure of the spread of repeated measurements either side of the mean. An advantage of the standard deviation over the variance is that its units are the same as those of the measurement. The standard deviation also allows you to determine how many significant figures are appropriate when reporting...
Note that a single value, or a mean value without any indication of the sample variance or standard deviation, is scientifically meaningless. Note also that the standard deviation determines the least significant digit (i.e. the correct number of significant figures) for the result. Finally, remember that both the standard deviation and variance ha...
These will have different magnitudes and signs, and result in a spread or dispersion of the measured values from the true value. An example would be any electronic measuring device – random electrical noise within its electronic components will cause the reading to fluctuate, even if the signal it is measuring is completely constant. Random error...
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Nov 5, 2013 · There are three ways in which the statistical information that accompanies a measurement (average, standard deviation, and confidence limit) can be stated. If, for example, five replicate measurements of a solid’s density were made, and the average was 1.015 g/cm 3 with an estimated standard deviation of 0.006, then the results of this ...
Jun 4, 2020 · Standard deviation: The standard deviation (denoted σ) also provides a measure of the spread of repeated measurements either side of the mean. An advantage of the standard deviation over the variance is that its units are the same as those of the measurement.
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The relative standard deviation between laboratories increases as the level of analyte decreases. At the ultratrace level of 1 ppb, interlaboratory error (%RSD) is nearly 50%.
