Name: mean, median, range, precision & accuracy
Uploaded: 2024-04-04T10:51:11.000Z
Duration: 1 min 11 s
Channel: JoVE

K12 Standards

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Earth Science

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Statistical Analysis: Overview

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single value. The difference between the obtained results and the true or expected value, or the central value, is known as the error in that measurement.
The central value in a set of scattered results is the estimated mean or median.
The Mean is the ratio between the sum and the total number of replicate measurement values. Alternatively, the median is the middle value amongst the records, arranged in an increasing or decreasing order.
The range is the numerical difference between the largest and smallest values in the replicate measurements.
Precision indicates the closeness between different replicate measurements. Accuracy reflects the closeness of a measurement to the true or central value.
Statistical analysis can categorize and characterize the results of an analysis to make an objective decision about data quality.

statistical analysis: overview

When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the total number of results. Another commonly used quantifier is the median, which is the middle value amongst all the results arranged in the increasing or decreasing order of their numerical values. In the presence of extremely large or small values in the data set, the median can be a more suitable measure for the data set overall. Both the mean and median can be useful measures of the central value of a set of measurements. In addition to the central value, the range is another way to characterize the distribution of a set of values. It is the numerical difference between the highest and lowest values in a set of results.
Precision and accuracy are two important measures of observed errors in the data set. Precision is the measure of closeness between the replicate measurements. In a precise data set, the values of different measurements cluster close together. The values are farther apart or more scattered in an imprecise data set. Often, the range of an imprecise data set will be high. On the other hand, accuracy is a measure of closeness between the measurements and the true or expected value. This means that the magnitude of errors in a more accurate data set is smaller than that of a less accurate data set.

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

Education

JoVE Core

Analytical Chemistry

Unit 1

Chemical Applications of Statistical Analyses

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

mean, median, range, precision & accuracy

Statistical analysis helps compare repeated measurements and judge how good the results are. When the same sample is measured again and again, small differences can appear. These differences are called errors. Researchers use statistics to describe the data and to decide whether a method is suitable.

The mean and median are common ways to find the central value of a data set. The mean is the sum of all results divided by the total number of results. The median is the middle value after the results are arranged in order. If a data set has very large or very small values, the median may describe the overall set better.

The range is another way to describe the spread of results. It is the difference between the highest value and the lowest value in the set. A large range often shows that the values are more scattered.

Precision and accuracy are two key ways to describe error. Precision means repeated measurements are close to one another, so the values cluster together. Accuracy means the measurements are close to the true or expected value. A more precise data set usually has a smaller spread, while a more accurate data set has smaller errors.

Mean, Median, Range, Precision & Accuracy

si units: 2019 redefinition

SI Units in Chemistry Measurements

SI units give chemistry measurements a common standard. A measurement has two parts: a number that shows magnitude and a unit that gives the comparison scale. Using the same unit system helps keep results consistent and reduces mistakes in scientific communication. The Système International d'Unités, or SI units, includes both fundamental units and derived SI units. Fundamental units describe base physical quantities such as mass, distance, temperature, time, electric current, luminous...

degrees of freedom

Degrees of Freedom in Statistical Calculations

Degrees of freedom describe how many values in a statistical calculation are free to vary. They represent the minimum number of independent numbers needed to determine a statistic. In a data set, some values may be independent while others depend on them. A simple example uses three unknown numbers with a mean of 10. The first two numbers can be chosen freely. The last number cannot be chosen on its own because it must keep the mean at 10. In that case, the data set has two degrees of freedom.<br...

Statistical analysis helps compare repeated measurements and judge how good the results are. When the same sample is measured again and again, small differences can appear. These differences are called errors. Researchers use statistics to describe the data and to decide whether a method is suitable. The mean and median are common ways to find the central value of a data set. The mean is the sum of all results divided by the total number of results. The median is the middle value after the...

types of errors: detection and minimization

types-of-errors-detection-and-minimization

Measurement Errors: Sources and Examples

Measurement errors are the differences between an obtained result and the true value or estimated central value. They can be written as absolute error or relative error. Absolute error is the numerical difference from the true or central value. Relative error compares that difference to the true or central value and is often shown as a percentage. Errors can also be grouped by their source, magnitude, and sign. In many experiments, the main categories are systematic, random, and gross errors.

systematic error: methodological and sampling errors

systematic-error-methodological-and-sampling-errors

Reducing Bias in Measurement Errors

Systematic errors are bias in measurement, and their sources can often be identified and reduced. In this topic, the main categories are sampling, instrumental, methodological, and personal errors. Each one comes from a different part of the experiment, so each one needs a different fix. Sampling errors happen when the sampling method is poor or when the wrong population is chosen. These errors can be reduced by improving the sampling strategy. Better sample selection helps the results...

random error

Random Error in Measurements

Random error in measurements comes from uncontrollable variables that affect data from one trial to the next. These variables can include changes in the environment, imperfections in an instrument, or the natural variation of the thing being measured. Because the direction and size of the error can change from one measurement to the next, random error is hard to predict, estimate, or describe directly. Although random error is difficult to remove, its overall effect can be studied in a large...

standard deviation of calculated results

Reading Data Spread with Standard Deviation

Standard deviation describes how spread out data are around the mean. It helps show how tightly values cluster near the center and how far they sit from that central value. Many large data sets follow a Gaussian distribution, also called a normal distribution. A Gaussian distribution has a bell-shaped curve. The mean, or central value, appears in the middle, where the most frequent values are found. As data points move farther from the center, deviation increases and frequency decreases. The...

introduction to z scores

Reading z Scores for Outliers

z scores show how far a value is from the mean in standard deviation units. A z score, also called a standardized value, tells whether a data point sits above or below the mean, μ. Values larger than the mean have positive z scores, while values smaller than the mean have negative z scores. If x equals the mean, then the z score is zero. The z score scale is centered on zero. That means the mean of all z scores is zero, and their standard deviation is one. This makes z scores useful for...

uncertainty: overview

Measuring and Reporting Uncertainty

Uncertainty is part of analytical chemistry measurement. When repeated measurements are taken, random errors can cause the results to differ in small ways. These repeated values are compared with the estimated or expected value to judge how much uncertainty is present. Uncertainty is usually written after the estimated or expected value. It should also be reported with the correct number of significant figures, which are the digits needed to show a precise result. The possible variation from...

propagation of uncertainty from random error

propagation-of-uncertainty-from-random-error

How Uncertainty Changes in Calculations

Uncertainty changes as measurements move through calculations. In a multi-step experiment, each measurement adds some uncertainty. Because the steps happen one after another, the uncertainty from one step carries into the next step and affects the final result. The way uncertainty is combined depends on the math operation. For addition and subtraction, the final result is reported with absolute uncertainty. Absolute uncertainty is found as the square root of the sum of the absolute...

propagation of uncertainty from systematic error

propagation-of-uncertainty-from-systematic-error

Atomic Mass Uncertainty in Isotope Samples

Atomic mass can vary because different samples contain different isotope ratios. For oxygen, the measured atomic mass is a weighted average of the isotopic masses in that sample. A single sample may not match the true atomic mass of oxygen found across all oxygen molecules on Earth. That creates sampling error, which is a type of systematic error. This kind of uncertainty is not random. It is tied to the system being measured. Within the uncertainty range, the chance of finding a particular...

uncertainty: confidence intervals

Confidence Intervals and Sample Size

Confidence intervals show a range of values around a sample mean that may contain the true mean. They are written as a probability percentage. A 95% confidence interval means the statistician is 95% confident that the true mean lies within that range. The two ends of the range are called confidence limits. These limits are estimated from the sample mean, the standard deviation, and the statistical factor t, or t-score. The t-score depends on the number of degrees of freedom and the confidence...

significance testing: overview

Significance Testing in Analytical Chemistry

Significance testing helps analytical chemists decide whether a difference is meaningful or just caused by random error. It is used to test whether a claim about a parameter is valid. In analytical chemistry, it mainly helps determine whether a change between two values comes from determinate error or indeterminate error. A determinate error has a clear source. It may come from a change in the measurement protocol, the analyst, or the sample itself. These changes can create a deviation from...

identifying statistically significant differences: the f-test

identifying-statistically-significant-differences-the-f-test

Comparing Variance with the F-Test

The F-test compares variance in two data sets or compares a sample variance with a population variance. It helps decide whether an indeterminate error can explain a difference in the values. In statistics, variance shows how spread out the data are. The test assumes that the data set or sets are normally distributed. It also assumes that the data sets are independent of each other. These conditions must be met before the F-test is used. The F test statistic is found by dividing one variance...

comparing experimental results: student's t-test

comparing-experimental-results-student-s-t-test

Student's t-Test for Significance Checks

Student's t-test is a statistical tool for checking whether two means are different in a meaningful way. It can compare a sample mean with a population mean, or it can compare the means from two data sets. The test uses the mean, standard deviation, and number of measurements, along with a chosen confidence interval. The test statistic is then compared with a table of critical values at that confidence level. If the test statistic is smaller than the critical value, the null hypothesis is...

detection of gross error: the q test

Using the Q Test to Flag Outlier Data

The Q test helps identify outlier data points that sit far from the rest of a data set. In high school lab work, this can help students decide whether an unusual value should stay in the data or be removed. Outliers often come from gross errors, or human mistakes, and may not reflect the real result being measured. Some points that look like outliers may still reflect a true difference in the phenomenon being studied. In those cases, a statistical test can help judge whether the value should...

calibration curves: linear least squares

Using a Calibration Line to Find Unknowns

A calibration curve links an instrument's signal to known concentrations of a substance. Scientists use it to set response levels with standards. They can also fit an equation to the curve and use it to find the concentration of unknown samples. When the data make a straight line, the linear least-squares method is the standard way to fit the curve. This method finds the line that best matches the points by minimizing the sum of the squared differences between the predicted and actual values.

calibration curves: correlation coefficient

calibration-curves-correlation-coefficient

Interpreting Correlation in Calibration Curves

Calibration curves use the correlation coefficient, written as r, to show how strongly two variables are related and which direction the relationship takes. In a linear calibration curve, this value helps describe the association between the variables being compared. The correlation coefficient ranges from -1 to +1. A value of +1 means a perfect positive linear correlation, while -1 means a perfect negative correlation. A value of 0 means there is no correlation between the two variables. A...

correlation and regression

Using Regression to Measure Variable Links

Correlation and regression are used to study the relationship between two variables. Correlation shows how strongly the variables are associated. Regression helps describe that relationship with a line that can be used for prediction. In linear regression, the relationship is written as a correlation coefficient. This coefficient is shown as r and ranges from -1 to +1. A positive value means the variables move in the same direction. A negative value means they move in opposite directions. <br...

difference from background: limit of detection

difference-from-background-limit-of-detection

Limit of Detection and Quantification

The limit of detection, or LOD, is the smallest amount of analyte that can be distinguished from background noise. In measurement science, background noise is the natural signal in a sample that can interfere with the analyte signal. The LOD helps show whether a substance is present, but it does not usually give a reliable amount. The LOD is set at the concentration where the analyte signal is three times larger than the standard deviation of the blank signal. A blank is a sample without the...

quantifying and rejecting outliers: the grubbs test

quantifying-and-rejecting-outliers-the-grubbs-test

Grubbs Test for Spotting Data Outliers

The Grubbs test is a statistical way to spot a possible outlier in a data set. It is used when the data is assumed to follow a normal distribution. A Grubbs test helps decide whether one unusual numerical value should be treated as a true outlier. To run a two-tailed Grubbs test, first find the absolute difference between the questionable value and the mean. Then divide that difference by the sample standard deviation. The result is the Grubbs statistic, or G. Next, compare the calculated G...

what is anova?

ANOVA for Comparing Sample Means

ANOVA, or Analysis of Variance, is a statistical test used to compare the means of three or more samples. It was developed by Ronald Fisher in 1918. In high school statistics, ANOVA helps determine whether group averages are equal or whether at least one group is different. Before ANOVA is used, the samples should meet three key assumptions. The data should come from normally distributed samples. The samples should also be randomly and independently selected. In addition, the populations...

key terms and concepts

Learn how mean, median, range, precision, and accuracy help describe repeated measurements, show error, and judge data quality in science.

Mean, Median, Range, Precision & Accuracy | JoVE K12

analytical chemistry

JoVE Core Analytical Chemistry simplifies complex chemical principles by breaking them down into clear, engaging animations, making topics from SI Units to NMR spectroscopy more accessible and straightforward. Additionally, the scientist-in-action videos highlight the application of these concepts in real-world research conducted in laboratories globally.

Life Science

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LS.1.c

Physical Science

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PS.1.c

Physics

PH.1

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Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.2

CHEM.2.C

Specialised Topic in Science

112.51.c.1.

112.51.c.2.B.

PHYS.2

PHYS.2.C

Chemistry and Physics

IPC.2

IPC.2.C

Scientific Method

The scientific method is used to solve problems and explain phenomena. The development of the scientific method coincided with changes in philosophy ...

Scientific Laws and Theories

Scientific Laws

In science, a law is defined as a concise, verbal or mathematical, statement that summarizes a vast number of experimental observations. ...

The Scientific Method

The scientific method is a detailed, empirical problem-solving process used by biologists and other scientists. This iterative approach involves ...

Chemistry is an empirical science. Scientists often pose questions to understand the chemistry in everyday life and seek answers to these questions. To ...

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about ...

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed ...

Hypothesis: Accept or Fail to Reject?

The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, ...

The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• ask questions that arise from careful observation of phenomena, examination of a model or theory, or unexpected results, and/or to seek additional information
• determine which questions can be investigated within the scope of the school laboratory or field experience
• generate hypotheses based on research and scientific principles
• make hypotheses that specify what happens to a dependent variable when an independent variable is manipulated
• define design problems that involve the development of a process or system with multiple components and criteria

ES.1.a

Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

Correlation and Causation

Correlation and CausationStatistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. A ...

Demonstrating the Scientific Method with Tree Branches
ExpandObtain branches containing a few dozen typical leaves from five different local tree species. ...

Observation and Background Research
ExpandNOTE: The first two steps in the scientific process involve studying and observing natural phenomena of ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
• individually and collaboratively plan and conduct observational and experimental investigations
• plan and conduct investigations to test design solutions in a safe and ethical manner including considerations of environmental, social and personal effects
• select and use appropriate tools and technology to collect, record, analyze, and evaluate data

ES.1.b

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their ...

Statistical Significance

Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful ...

Review and Preview

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative ...

Data: Types and Distribution

In biostatistics, data refers to the collected observations that are subject to analysis. Data can be parametric or nonparametric.
Nonparametric data ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

Scatter Plot

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a ...

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show ...

Pie Chart

A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each ...

Numerical Calculations

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of ...

Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy ...

Significant Figures in Calculations

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be ...

Realism in Experimentation

Source: Laboratories of Gary Lewandowski, Dave Strohmetz, and Natalie Ciarocco&#8212;Monmouth University

In an ideal world researchers would conduct ...

The student will demonstrate an understanding of scientific and engineering practices by pnterpreting, analyzing, and evaluating data
• construct and interpret data tables showing independent and dependent variables, repeated trials, and means
• construct, analyze, and interpret graphical displays of data and consider limitations of data analysis
• apply mathematical concepts and processes to scientific questions
• use data in building and revising models, supporting explanations of phenomena, or testing solutions to problems
• analyze data using tools, technologies, and/or models in order to make valid and reliable scientific claims or determine an optimal design solution

Data Collection by Observations

Data collection refers to a systematic way of obtaining, observing, measuring, and analyzing accurate information. Observational studies are one of the ...

Data Collection by Experiments

Data collection is a systematic method of obtaining, observing, measuring, and analyzing accurate information. An experimental study is a standard method ...

Data Collection by Survey

The systematic method of obtaining and analyzing accurate information of a population is called data collection. A survey is a standard method of data ...

Reliability and Validity

Reliability and validity are two important considerations that must be made with any type of data collection. Reliability refers to the ability to ...

Reasoning

Reasoning involves transforming information into conclusions, which is essential for problem-solving, decision-making, and critical thinking.
Reasoning ...

The student will demonstrate an understanding of scientific and engineering practices by constructing and critiquing conclusions and explanations
• make quantitative and/or qualitative claims based on data
• construct and revise explanations based on valid and reliable evidence obtained from a variety of sources, including students' own investigations, models, theories, simulations, and peer review
• apply scientific ideas, principles, and/or evidence to provide an explanation of phenomena or design solutions
• construct arguments or counterarguments based on data and evidence
• differentiate between a scientific hypothesis, theory, and law

ES.1.d

using-topographic-maps-to-generate-topographic-profiles

Using Topographic Maps to Generate Topographic Profiles

Source: Laboratory of Alan Lester - University of Colorado Boulder
Topographic maps are &#34;plan-view&#34; representations of Earth&#39;s ...

The student will demonstrate an understanding of scientific and engineering practices by developing and using models
• evaluate the merits and limitations of models
• develop, revise, and/or use models based on evidence to illustrate or predict relationships
• construct and interpret scales, diagrams, classification charts, graphs, tables, imagery, models, including geologic cross sections and topographic profiles
• read and interpret topographic and basic geologic maps and globes, including location by latitude and longitude

ES.1.e

Data Source

A data source is the origin of collected data, whether physical or digital, and includes all channels, platforms, and repositories for gathering and ...

Communication

Sharing information, concepts, and emotions to foster mutual understanding is communication. The sender, recipient, and transaction must be considered in ...

levels-of-communication-i-intrapersonal-interpersonal-and-small-group

Levels of Communication I: Intrapersonal, Interpersonal, and Small Group

Interpersonal communication focuses on the exchange of messages between two people.
We can participate in these relationships through verbal, nonverbal, ...

levels-of-communication-ii-organizational-public-and-group-dynamics

Levels of Communication II: Organizational, Public, and Group Dynamics

Effective communication is the foundation of a good organization. Communication is the lifeblood of an organization that connects the group with messages. ...

The student will demonstrate an understanding of scientific and engineering practices by obtaining, evaluating, and communicating information
• compare, integrate, and evaluate sources of information presented in different media or formats to address a scientific question or solve a problem
• gather, read, and evaluate scientific and/or technical information from multiple sources, assessing the evidence and credibility of each source
• communicate scientific and/or technical information about phenomena and/or a design process in multiple formats

ES.1.f

Mean, Median, Range, Precision & Accuracy

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