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Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Random Error01:04

Random Error

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Propagation of Uncertainty from Systematic Error01:10

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Updated: Apr 30, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
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Visualization of uncertainty without a mean.

Kristin Potter, Samuel Gerber, Erik W Anderson

    IEEE Computer Graphics and Applications
    |May 9, 2014
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    Summary
    This summary is machine-generated.

    Entropy, an information-theoretic measure, quantifies uncertainty in categorical datasets. This study explores using entropy in data visualizations to better represent data complexity and uncertainty.

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    Area of Science:

    • Data Visualization
    • Information Theory
    • Computer Science

    Background:

    • Increasing dataset size and complexity necessitate methods to represent data uncertainty.
    • Current visualization techniques often struggle to adequately convey uncertainty.
    • Characterizing uncertainty for visualization purposes presents significant challenges.

    Purpose of the Study:

    • To demonstrate the utility of entropy as a quantifiable metric for uncertainty in categorical data.
    • To expand the range of available uncertainty measures for data visualization.
    • To provide a framework for interpreting and applying entropy in visualization contexts.

    Main Methods:

    • Mathematical formulation of entropy for uncertainty quantification.
    • Exploration of information-theoretic principles for visualization.
    • Analysis of entropy's application in categorical dataset visualizations.

    Main Results:

    • Entropy provides a robust mathematical basis for measuring uncertainty in categorical data.
    • The study outlines the interpretation and practical use of entropy within visualization frameworks.
    • Demonstrates entropy as a viable metric for enhancing uncertainty representation.

    Conclusions:

    • Entropy is a valuable metric for visualizing uncertainty in complex datasets.
    • Integrating entropy expands the toolkit for data scientists and visualization experts.
    • This research contributes to more accurate and informative data representations.