Technology Tips: Visual Representations of Mean and Standard Deviation

1996 ◽  
Vol 89 (8) ◽  
pp. 688-692
Author(s):  
Charles Vonder Embse ◽  
Arne Engebretsen
Keyword(s):  
Standard Deviation ◽  
Visual Representations ◽  
Visual Display ◽  
Graphing Calculators ◽  
Statistical Information ◽  
Summary Statistics ◽  
Data Set ◽  
The Mean ◽  
Nonparametric Statistical ◽  
Bar Graphs

Summary statistics used to describe a data set are some of the most commonly taught statistical concepts in the secondary curriculum. Mean, median, mode, range, and standard deviation are topics that can be found in nearly every program. Technology empowers us to access these concepts and easily to create visual displays that interpret and describe the data in ways that enhance students' understanding. Many graphing calculators allow students to display nonparametric statistical information using a box-and-whiskers plot or a modified box plot showing a visual representation of the median, upper and lower quartiles, and the range of the data. But how can students visually display the mean of the data or show what it means to be within one standard deviation of the mean? One way to create this type of visual display is with a bar graph and constant functions. Unfortunately, graphing calculators, and some computer programs, only display histograms and not bar graphs. The tips in this issue focus on using graphing calculators to draw bar graphs that can help students visualize and interpret the mean and standard deviation of a data set.

scholarly journals Section 3: Preliminary Analysis of the Results

Radiocarbon ◽  
2003 ◽  
Vol 45 (2) ◽  
pp. 159-174
Keyword(s):  
Standard Deviation ◽  
Statistical Methods ◽  
Standard Error ◽  
Preliminary Analysis ◽  
Exploratory Analysis ◽  
Initial Evaluation ◽  
Summary Statistics ◽  
The Mean

In this section, we present the exploratory analysis of the results submitted by the extended deadline of December 2000. We first deal with Samples C.J, before considering the near-background samples A and B (Kauri wood). The aims of the exploratory analysis are to discover the range of results reported for each sample and the initial evaluation of the effects of any factors that might be a source of variation in the results. For each sample, in turn, we consider the main summary statistics.the number of results reported (N), their mean or average, median, the standard deviation (StDev), the standard error of the mean (Sem), the quartiles (25th [Q1] and 75th [Q3] percentiles), and the minimum (Min) and maximum (Max)—before graphically studying the overall distribution of results in the form of a boxplot, with a view to identifying any extreme or outlying observations. The summary statistics and distribution of results for each laboratory type are also shown. Further details on the statistical methods used are contained in Appendix 3.

scholarly journals Validation of SCIAMACHY HDO/H<sub>2</sub>O measurements using the TCCON and NDACC-MUSICA networks

2015 ◽  
Vol 8 (4) ◽  
pp. 1799-1818 ◽  
Author(s):  
R. A. Scheepmaker ◽  
C. Frankenberg ◽  
N. M. Deutscher ◽  
M. Schneider ◽  
S. Barthlott ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Hydrological Cycle ◽  
Source Region ◽  
Total Carbon ◽  
Atmospheric Composition ◽  
The Tibetan Plateau ◽  
Wet Season ◽  
Data Set ◽  
The Mean ◽  
The Impact

Abstract. Measurements of the atmospheric HDO/H2O ratio help us to better understand the hydrological cycle and improve models to correctly simulate tropospheric humidity and therefore climate change. We present an updated version of the column-averaged HDO/H2O ratio data set from the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY). The data set is extended with 2 additional years, now covering 2003–2007, and is validated against co-located ground-based total column δD measurements from Fourier transform spectrometers (FTS) of the Total Carbon Column Observing Network (TCCON) and the Network for the Detection of Atmospheric Composition Change (NDACC, produced within the framework of the MUSICA project). Even though the time overlap among the available data is not yet ideal, we determined a mean negative bias in SCIAMACHY δD of −35 ± 30‰ compared to TCCON and −69 ± 15‰ compared to MUSICA (the uncertainty indicating the station-to-station standard deviation). The bias shows a latitudinal dependency, being largest (∼ −60 to −80‰) at the highest latitudes and smallest (∼ −20 to −30‰) at the lowest latitudes. We have tested the impact of an offset correction to the SCIAMACHY HDO and H2O columns. This correction leads to a humidity- and latitude-dependent shift in δD and an improvement of the bias by 27‰, although it does not lead to an improved correlation with the FTS measurements nor to a strong reduction of the latitudinal dependency of the bias. The correction might be an improvement for dry, high-altitude areas, such as the Tibetan Plateau and the Andes region. For these areas, however, validation is currently impossible due to a lack of ground stations. The mean standard deviation of single-sounding SCIAMACHY–FTS differences is ∼ 115‰, which is reduced by a factor ∼ 2 when we consider monthly means. When we relax the strict matching of individual measurements and focus on the mean seasonalities using all available FTS data, we find that the correlation coefficients between SCIAMACHY and the FTS networks improve from 0.2 to 0.7–0.8. Certain ground stations show a clear asymmetry in δD during the transition from the dry to the wet season and back, which is also detected by SCIAMACHY. This asymmetry points to a transition in the source region temperature or location of the water vapour and shows the added information that HDO/H2O measurements provide when used in combination with variations in humidity.

scholarly journals The shifting boxplot. A boxplot based on essential summary statistics around the mean.

2010 ◽  
Vol 3 (1) ◽  
pp. 37-45 ◽  
Author(s):  
Fernando Marmolejo-Ramos ◽  
Tian Siva Tian
Keyword(s):  
Interquartile Range ◽  
Summary Statistics ◽  
Scientific Applications ◽  
Data Set ◽  
Report Data ◽  
Graphical Technique ◽  
The Mean

Boxplots are a useful and widely used graphical technique to explore data in order to better understand the information we are working with. Boxplots display the first, second and third quartile as well as the interquartile range and outliers of a data set. The information displayed by the boxplot, and most of its variations, is based on the data’s median. However, much of scientific applications analyse and report data using the mean. In this paper, we propose a variation of the classical boxplot that displays information around the mean. Some information about the median is displayed as well.

Comparing Baseline and Intervention Phases

2021 ◽  
pp. 57-89
Author(s):  
Charles Auerbach
Keyword(s):  
Standard Deviation ◽  
Effect Size ◽  
Visual Analysis ◽  
Descriptive Statistics ◽  
Data Set ◽  
Standard Methods ◽  
Intervention Phase ◽  
Box Plots ◽  
The Mean ◽  
Two Phases

In this chapter readers will learn about methodological issues to consider in analyzing the success of the intervention and how to conduct visual analysis. The chapter begins with a discussion of descriptive statistics that can aid the visual analysis of findings by summarizing patterns of data across phases. An example data set is used to illustrate the use of specific graphs, including box plots, standard deviation band graphs, and line charts showing the mean, median, and trimmed mean that can used to compare any two phases. SSD for R provides three standard methods for computing effect size, which are discussed in detail. Additionally, four methods of evaluating effect size using non-overlap methods are examined. The use of the goal line is discussed. The chapter concludes with a discussion of autocorrelation in the intervention phase and how to consider dealing with this issue.

scholarly journals Effects of Secular Changes in Frequency of Observations and Observational Errors on Monthly Mean MSLP Summary Statistics Derived from ICOADS

2005 ◽  
Vol 18 (17) ◽  
pp. 3623-3633 ◽  
Author(s):  
Edmund K. M. Chang
Keyword(s):  
Standard Deviation ◽  
Reanalysis Data ◽  
Summary Statistics ◽  
Observational Error ◽  
Error Statistics ◽  
Cyclone Activity ◽  
Data Set ◽  
Sea Level Pressure ◽  
Increasing Trend ◽  
Order Of Magnitude

Abstract A Monte Carlo technique has been employed to assess how sextile mean sea level pressure (MSLP) statistics derived from ship observations can be affected by changes in the frequency of observations. The results show that when the number of observations is small (less than 20 per month), the estimates of the first sextile as well as the intersextile range, which is considered to be a resistant estimate of the standard deviation, can contain large biases. The results also suggest that, while changes in the frequency of observations do not have strong impacts on the standard way of estimating the standard deviation, such statistics are strongly affected by secular trends in observational error statistics. The results are applied to examine the increasing trend in cool season (December–March) Pacific cyclone activity during the second half of the twentieth century. The results show that the trends in sextile statistics derived from the NCEP–NCAR reanalysis data are only consistent with those derived from the International Comprehensive Ocean–Atmosphere Data Set (ICOADS) summary statistics if biases due to changes in the frequency of observation are not taken into account. When such biases are accounted for, the trends derived from the observations are significantly smaller than those derived from the reanalysis data. As for the increasing trend in MSLP variance, the trends derived from the ICOADS statistics are smaller than those derived from the reanalysis regardless of whether corrections are made to account for the secular trend in MSLP error statistics. In either case, the corrections that have to be applied have the same order of magnitude as the observed trends. The two main conclusions are that 1) climate statistics can be strongly affected by changes in frequency of observations as well as changes in observational error statistics and 2) the trends in North Pacific winter cyclone activity, as derived from NCEP–NCAR reanalysis data, appear to be significantly larger than similar trends computed from ICOADS sextile and variance statistics, when biases due to changes in frequency of observations and observational error statistics have been taken into account.

Using Skew for Classification

2015 ◽  
Vol 29 (03) ◽  
pp. 1551002
Author(s):  
Mark J. DeBonis
Keyword(s):  
Distribution Function ◽  
Standard Deviation ◽  
Probability Distribution ◽  
Principle Component Analysis ◽  
Probability Distribution Function ◽  
Error Rates ◽  
Binary Classifier ◽  
Data Set ◽  
Principle Component ◽  
The Mean

One classic example of a binary classifier is one which employs the mean and standard deviation of the data set as a mechanism for classification. Indeed, principle component analysis has played a major role in this effort. In this paper, we propose that one should also include skew in order to make this method of classification a little more precise. One needs a simple probability distribution function which can be easily fit to a data set and use this pdf to create a classifier with improved error rates and comparable to other classifiers.

scholarly journals Technical note: analytical estimation of the optimal parameters for the EOF retrievals of the IASI Level 2 Product Processing Facility and its application using AIRS and ECMWF data

2006 ◽  
Vol 6 (3) ◽  
pp. 831-846 ◽  
Author(s):  
X. Calbet ◽  
P. Schlüssel
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Mean Difference ◽  
Training Data ◽  
Data Set ◽  
The Real ◽  
Atmospheric Profiles ◽  
The Mean ◽  
Atmospheric State ◽  
The Difference

Abstract. The Empirical Orthogonal Function (EOF) retrieval technique consists of calculating the eigenvectors of the spectra to later perform a linear regression between these and the atmospheric states, this first step is known as training. At a later stage, known as performing the retrievals, atmospheric profiles are derived from measured atmospheric radiances. When EOF retrievals are trained with a statistically different data set than the one used for retrievals two basic problems arise: significant biases appear in the retrievals and differences between the covariances of the training data set and the measured data set degrade them. The retrieved profiles will show a bias with respect to the real profiles which comes from the combined effect of the mean difference between the training and the real spectra projected into the atmospheric state space and the mean difference between the training and the atmospheric profiles. The standard deviations of the difference between the retrieved profiles and the real ones show different behavior depending on whether the covariance of the training spectra is bigger, equal or smaller than the covariance of the measured spectra with which the retrievals are performed. The procedure to correct for these effects is shown both analytically and with a measured example. It consists of first calculating the average and standard deviation of the difference between real observed spectra and the calculated spectra obtained from the real atmospheric state and the radiative transfer model used to create the training spectra. In a later step, measured spectra must be bias corrected with this average before performing the retrievals and the linear regression of the training must be performed adding noise to the spectra corresponding to the aforementioned calculated standard deviation. This procedure is optimal in the sense that to improve the retrievals one must resort to using a different training data set or a different algorithm.

Observations on the Correlation between Statistics of some Fatigue Crack Growth Data and Applied Loads for 2024-T351

2011 ◽  
Vol 197-198 ◽  
pp. 1626-1630
Author(s):  
Chih Chung Ni
Keyword(s):  
Fatigue Crack ◽  
Standard Deviation ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Applied Stress ◽  
Stress Amplitude ◽  
Logarithmic Scale ◽  
Growth Data ◽  
Data Set ◽  
The Mean

Three sets of fatigue crack growth data tested under different constant-amplitude loads for CT specimens made of 2024 T-351 aluminum alloy are released, and the analyzed results presented in this study are specially emphasized on the correlation between statistics of these scattered fatigue data and their applied loads. Investigating the scatters of initiation cycle and specimen life, it was found that both the mean and standard deviation of initiation cycle, as well as the mean and standard deviation of specimen life, decrease as applied stress amplitude increases. Moreover, the negatively linear correlation between the median values of initiation cycle and applied stress amplitudes presented in linear scale, and between the median values of specimen life and applied stress amplitudes presented in logarithmic scale were found, where the initiation cycle and specimen life are all best depicted by normal distributions for all three data sets. Finally, the mean of intercepts and mean of exponents of Paris-Erdogan law for each data set were studied, and it was found that the mean of intercepts decreases greatly as applied stress amplitude increases, while the mean of exponents decreases slightly.

scholarly journals Factors Influencing Nurse Burnout and Recommendations

2018 ◽  
Author(s):  
Eddy Alecia Love Lavalais ◽  
Tayler Jackson ◽  
Purity Kagure ◽  
Myra Michelle DeBose ◽  
Annette McClinton
Keyword(s):  
Quality Improvement ◽  
Standard Deviation ◽  
Emotional Exhaustion ◽  
Maslach Burnout Inventory ◽  
Personal Accomplishment ◽  
Combat Stress ◽  
Data Set ◽  
Factors Influencing ◽  
Nurse Burnout ◽  
The Mean

Background: Identifying nurse burnout to be of significance, as it directly impacts work ethic, patient satisfaction, safety and best practice. Nurses are more susceptible to fatigue and burnout, due to the fact of working in highly stressful environments and caring for people in their most vulnerable state. It is imperative to pinpoint and alleviate potential aspects that can lead to nurse burnout. Research Hypothesis: Educating nurses on recognizing factors influencing nurse burnout and offering effective interventions to combat stress, will lead to better coping and adaptation skills; hence, decreasing the level of nurse fatigue and burnout. Assisting nurses to be cognizant of the symptoms of stress and nurse burnout will lead to the development of positive adaptive mechanisms. However, nurses without this recognition, tend to develop maladaptive psychological skills. Research Methodology: The quality improvement project gathered data on factors influencing burnout via Maslach Burnout Inventory Tool (MBI). MBI is the most commonly used instrument in measuring burnout, by capturing three subscales of burnout: emotional exhaustion (EE), depersonalization (DP) and personal accomplishment (PA). Results: From a sample of 31 graduate nursing (employed) students, MBI survey was administered via survey monkey. Gathered data (n=31), via descriptive statistics and standard deviation, represented the extent of deviation for the nursing population as a whole. The quality improvement study revealed the standard deviation (SD) for emotional exhaustion, a low SD of 0.3; indicating that data points appear to be closer to the mean (expected value) of the emotional exhaustion data set. Additionally, depersonalization data showed SD values that were widely spread; however, yielding a low SD of 0.42 from the mean on depersonalization. Lastly, higher scores derived from Maslach’s Burnout Inventory tool suggests increased levels of personal accomplishment. Thus, data set revealed lower levels of depersonalization in regards to sample size.  Moreover, Pearson correlation coefficient (Pearson r) identified a positive correlation between independent variable of stress levels and factors influencing nurse burnout, with combined teaching of ways to combat stress in the workplace. Effectiveness of this was reported by ninety-eight percent (98%) of participants. Significance: This study maintains that limited emotional exhaustion, a strong sense of identity and achieving personal accomplishments minimizes burn out.

scholarly journals Complete recovery of values in Diophantine systems (CORVIDS)

2018 ◽  
Author(s):  
Sean Wilner ◽  
Katherine Wood ◽  
Daniel J. Simons
Keyword(s):  
Standard Deviation ◽  
Open Source ◽  
Diophantine Equations ◽  
Source Code ◽  
Complete Recovery ◽  
Summary Statistics ◽  
Data Set ◽  
Raw Data ◽  
Source Program ◽  
User Friendly

Raw data are often unavailable, and all that may remain of a data set are its summary statistics. When these data are integers on a fixed scale, such as Likert-style ratings, and their mean, standard deviation, and sample size are known, it is possible to reconstruct every raw distribution that gives rise to those summary statistics using a system of Diophantine equations. We have developed the open-source program CORVIDS (COmplete Reconstruction of Values In Diophantine Systems) to deterministically reconstruct raw data from summary statistics using this technique. The solutions generated by the program are provably complete. Here we describe the implementation, provide examples and use cases, and prove the correctness of the underlying mathematics. CORVIDS is open-source and available as source code or as stand-alone, user-friendly applications for macOS and Windows.

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