Chapter 11: Random Errors in Chemical Analysis Flashcards
what do the accumulated effect of the individual uncertainties cause
replicate results to fluctuate randomly around the mean of the set
symmetric and unimodal (i.e., a single peak) with tails that appear to extend to positive and negative infinity
- Gaussian curve or
- Normal error curve
difference between the highest and lowest result in a set of replicate measurements
spread
- graph that shows the frequency of numerical data using rectangles
- height of a rectangle (the vertical axis) represents the distribution frequency of a variable (the amount, or how often that variable appears)
histogram
where do we base statistical analyses
assumption that random errors in analytical results follow a Gaussian, or normal, distribution
collection of all measurements of interest to the experimenter
population
subset of measurements selected from the population
sample
two parameters that describe Gaussian curves
- population mean µ
- population standard deviation σ
refers to quantities that define a population or distribution
parameters
refers to an estimate of a parameter that is made from a sample of data
statistic
difference between x̄ and µ
is neglible by the time N reaches what
20 to 30
measure of the precision of the population
standard deviation σ
General Properties of the Normal Curve
- mean occurs at central point of maximum frequency
- symmetrical distribution of positive and negative deviations about the maximum
- exponential decrease in frequency as the magnitude of deviations increases. Small uncertainties are observed much more often than very large ones
__ of area beneath Gaussian curve for population lies within one standard deviation
68.3%
__ of all data points are within +_2σ
95.4%
