Understanding Gaussian Distribution and Statistical Analysis Concepts

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Chemistry - Analytical Chemistry

user_lira_cofre Created by 9 mon ago

Cards in this deck(100)

Experimental measurements subject to random errors follow a _____ distribution.

What exists in every measurement due to inherent variability? _____

Why can random errors never be totally eliminated? Because the many sources of small individual random errors _____ be identified.

The accumulated effect of the individual uncertainties causes replicate measurements to _____ randomly around the mean of the set.

The sources of random errors can be small changes in _____ or pressure, random responses of electronic detectors.

A symmetrical bell-shaped curve that represents the distribution of values, frequencies, or probabilities of a set of data is called a _____ curve.

What is a Gaussian curve? It is a symmetrical bell-shaped curve that represents the distribution of _____, frequencies, or probabilities of a set of data.

If an experiment is done a large number of times, the resulting values tend to cluster around an average value in a symmetric fashion. Many repetitions result in a _____ curve.

Sources of random uncertainties in the calibration of a pipet include visual judgement, temperature fluctuations, and variations in the _____ time.

Ordinarily, random errors in analytical results follow a _____ distribution.

Ordinarily, _____ errors in analytical results follow a Gaussian distribution.

Statistical analysis reveals only _____ that is already present in a data set.

Statistical analysis reveals only information that is already present in a _____ set.

No new information is created by _____ treatments.

Statistical methods allow us to categorize and characterize data in different ways and to make _____ and intelligent decisions about data quality and interpretation.

_____ methods allow us to categorize and characterize data in different ways and to make objective and intelligent decisions about data quality and interpretation.

In scientific studies, we infer information about a population or universe from observations made on a _____ or sample.

The _____ is the set of all objects in the system we are investigating.

What is the population? It is the set of all _____ in the system we are investigating.

A _____ is a subset of measurements selected from the population.

What is a sample? It is a subset of _____ selected from the population.

What is the difference between a statistical sample and an analytical sample? A statistical sample is used to make inferences about the entire population, while an analytical sample is a portion of material taken for _____ analysis.

The properties of Gaussian curves are defined in terms of the _____ of the population.

Gaussian Curves can be described by an equation that contains just two parameters. What are they? _____ mean and population standard deviation.

The _____ mean is the arithmetic average of a limited sample drawn from a population of data.

How do you find the sample mean? You _____ all values then divide by the number of values.

The _____ mean is the true mean for the population.

When does the sample mean approximately equal the population mean? When N is greater than or equal to _____

The population standard deviation is a measure of _____ of a population of data.

What symbol represents population standard deviation? _____ or sigma.

A Gaussian curve with unit area is called a _____ error curve.

What is a normal error curve? It is a Gaussian curve with _____ area.

The breadth of these normal error curves is a measure of the _____ of the data sets.

For a normal error curve, a smaller breadth indicates _____ data.

The _____-variable describes the deviation of a data point from the mean relative to the standard deviation.

What does a z-variable describe? It describes the deviation of a data point from the mean relative to the _____ deviation.

A plot of relative frequency versus z yields a single Gaussian curve that describes all populations of data regardless of _____ deviation.

What are the several features of a Gaussian curve? The mean occurs at the central point of maximum frequency, there is a symmetrical distribution of positive and negative deviations about the maximum, and there is an exponential decrease in frequency as the magnitude of the deviations increases. Thus, small uncertainties are observed much more often than very _____ ones.

The area under a Gaussian curve is an important and useful property as it is equal to the _____ of finding a member of the population with a particular range of values.

_____ of the area under a Gaussian curve for a population lies within one standard deviation (+1s) of the mean value.

Standard deviation of a population of data is a predictive tool because of the _____ relationship.

A sample standard deviation is an _____, based on a sample, of a population standard deviation.

A sample standard deviation is an estimate, based on a sample, of a _____ standard deviation.

s is a measure of the _____ of a sample of data.

N-1 is called the number of _____ of freedom.

The number of degrees of freedom is the number of independent _____ available to fit a model to data.

The _____ error of the mean is the uncertainty of the average value.

What is the standard error of the mean? It is the _____ of the average value.

Describe the relationship between the standard error of the mean and the standard deviation. The standard error of the mean is _____ than the standard deviation.

Standard deviation describes the _____ between individuals in a sample.

What does standard deviation describe? It describes the _____ between individuals in a sample.

The standard error of the mean describes the _____ of how the sample mean represents the population mean.

What does the standard error of the mean describe? It describes the _____ of how the sample mean represents the population mean.

The standard error of the mean is the standard deviation of a set of data divided by the square root of the _____ of data points in the set.

How do you calculate the standard error of the mean? You divide the standard deviation by the square root of _____

The standard error is smaller than the standard deviation by a factor of _____

If we have several subsets of data, we can get a better estimate of the population standard deviation by _____ the data.

The pooled standard deviation is a _____ average of the individual estimates.

What is the pooled standard deviation? It is a _____ average of the individual estimates.

What are the terms to report the precisions of the data in analytical work? Sample standard deviation, variance, spread or range, relative standard deviation, and _____ of variation.

What is the symbol for sample standard deviation? _____

What is the symbol for variance? _____

What is the symbol for spread or range? _____

What is the symbol for relative standard deviation? _____

What is the symbol for coefficient of variation? _____

Variance is the _____ of the standard deviation.

What is variance? It is the _____ of the standard deviation.

The sample variance s^2 is an estimate of the _____ variance.

RSD is often expressed in _____ or percent.

How do you calculate the relative standard deviation? You divide the sample standard deviation by the _____

The coefficient of variation is the relative standard deviation multiplied by _____

The coefficient of variation is the relative standard deviation multiplied by _____%

The spread or range is the difference between the _____ and smallest values in the set.

What is the spread or range? It is the difference between the _____ and smallest values in the set.

Propagation of error describes how to use the measurement uncertainties to estimate the _____ in the calculated result.

The significant figures in a number are all of the digits known with certainty plus the first _____ digit.

All non-zero digits are _____

Interior zeros are _____

Leading zeros are _____

Trailing zeros after a decimal point are _____

Zeros at the end of a number without a written decimal point are _____

When adding and subtracting numbers in scientific notation, express the numbers to the lowest number of _____ places present and to the same power of 10.

When using multiplication and division, the answer can be no more precise than the _____ precise number from which the answer is derived.

It is seldom justifiable to keep more than one significant figure in the _____ deviation.

It is particularly important to postpone rounding until the _____ is complete.

At least one extra digit beyond the significant digits should be carried through all of the computations in order to avoid a _____ error.

The spread is the difference between the _____ and lowest result.

A Gaussian, or normal error, curve is a curve that shows the symmetrical distribution of data around the _____ of an infinite set of data.

Experiments in which the outcome is either a success or failure are called _____ experiments.

Experiments in which the outcome is either a success or failure are binomial experiments that follow a _____ distribution.

A _____ distribution occurs for a series of discrete events where the average time between events is known, but the exact timing is random.

A _____ refers to an estimate of a parameter that is made from a sample of data.

The sample mean is the sum of the measurement values divided by the _____ of measurements as given.

If there is no systematic error in the population, the population mean is the _____ value for the measured quantity.

The probable difference between the sample mean and population mean decreases rapidly as the number of measurements making up the sample _____

The sample mean is a statistic that estimates the population parameter, _____ mean.

The z-variable represents the deviation of a result from the population mean relative to the _____ deviation.

Because it appears in the Gaussian error curve expression, the square of the standard deviation (sigma^2) is also important. This quantity is called the _____

Never round a standard deviation calculation until the _____

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