Chapter 4: Random Errors in Chemical Analysis Flashcards
these types of errors are caused by the many uncontrollable variables that accompany every measurement.
random errors
TRUE or FALSE
Usually, most contributors
to random error cannot be positively identified. Even if we can identify random error sources, it is often impossible to measure them because most are so small that they cannot be detected individually
TRUE
A ____________ is a bar graph such as
that shown by plot A
histogram
is a curve that shows the symmetrical
distribution of data around the mean
of an infinite set of data
Gaussian, or normal error, curve
The frequency distribution data is plotted as a
bar graph or histogram
sources of random uncertainties in the calibration of a pipet
visual judgments
variations in drainage time & drainage angle
temperature fluctuations
vibrations and drafts
Experiments in which the outcome
is either a success or failure are
binomial experiments that follow a
binomial distribution
occurs for a series of
discrete events where the average
time between events is known, but
the exact timing is random.
Poisson distribution
is the collection of
all measurements of interest to the
experimenter
population
is a subset of measurements selected from
the population.
sample
TRUE or FALSE
Generally, we base statistical analyses on the assumption that random errors in analytical results follow a Gaussian, or normal, distribution. Also, analytical data can follow other distributions other than the Gaussian distribution.
TRUE
experiments in which there is either a successful outcome or a failure produce data that follow the
binomial distribution
Radioactive or photon-counting experiments produce results that follow the
Poisson distribution
is the collection of all measurements of interest and must be carefully defined by the experimenter. In some cases, it is defined as finite and real, while in others, it is hypothetical or conceptual in nature
population
TRUE or FALSE
Typically in a scientific study, we infer information about a population or universe from observations made on a subset or sample.
TRUE
refers to quantities such as m and s that define a population or distribution
parameter
refers to an estimate of
a parameter that is made from a sample of data
statistic
Example of statistics that estimate parameter
sample mean
sample standard deviation
the arithmetic average of a limited sample drawn from a population of data
sample mean
is defined as the sum of the measurement values divided by the number of measurements as given
sample mean
is defined as the true mean for the population
population mean
TRUE or FALSE
If there is no systematic error in the population, the population mean is also the true value for the measured quantity
TRUE
TRUE or FALSE
the sample mean x is a statistic that estimates the population parameter m.
TRUE
is a measure of the precision of the
population is given by summing the squares of the deviations from the mean, dividing by the number of measurements N, and taking the square root of the result
population standard deviation
normal error curve has several general properties including
mean occurs at the central point of max frequency
symmetrical distribution of positive and negative deviations about the maximum
exponential decrease in frequency as magnitude of the deviations increases
square of the standard deviation in a population is caled as
variance
square of the standard deviation in a sample is caled as
sample variance
indicates the number of independent results that enter into the computation of the standard deviation. It is also represented as N-1.
number of degrees of freedom
TRUE or FALSE
When m is unknown, two
quantities must be extracted from a set of replicate data: x and s.
TRUE
TRUE or FALSE
never round a standard deviation calculation until the very end.
TRUE
TRUE or FALSE
As N becomes larger, x and s become better estimators of m and s.
TRUE
The standard deviation of each mean is known as the
standard error of
the mean (Sm)
TRUE or FALSE
The standard error of a mean, sm,
is the standard deviation of a set
of data divided by the square root
of the number of data points in
the set.
TRUE
TRUE or FALSE
If we have several subsets of data, a better estimate of the population standard
deviation can be obtained by pooling (combining) the data instead of using
only one data set.
TRUE
is a weighted average of the individual estimates.
Spooled
is just the square of the standard deviation
variance
is an estimate of the population variance
sample variance
TRUE or FALSE
The advantage of using variance is that variances are additive in many situations,
TRUE
formula for relative standard deviation
RSD= st= s/mean
RSD multiplied by 100% is called the
coefficient variation
is another term that is sometimes used to describe the precision of a set of replicate results. It is the difference between the largest value in the set and the smallest
spread or range
TRUE or FALSE
the absolute standard deviation of the logarithm of a number is determined
by the relative standard deviation of the number; conversely, the relative
standard deviation of the antilogarithm of a number is determined by the absolute
standard deviation of the number
TRUE
The__________ in a number
are all the certain digits plus the first
uncertain digit
significant figures
TRUE or FALSE
It is especially important to postpone rounding until the calculation is completed
TRUE
At least one extra digit beyond the significant digits should be carried through all the
computations in order to avoid a rounding error, which is called
guard digit
