Stem - and - leaf display - wikipedia Stem - and - leaf display Time table using a stem - and - leaf layout at Minato Mirai train station in Yokohama, Japan. It is a widespread design pattern in the country. A stem - and - leaf display or stem - and - leaf plot is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley 's work in the early 1900s, and are useful tools in exploratory data analysis. Stemplots became more commonly used in the 1980s after the publication of John Tukey 's book on exploratory data analysis in 1977. The popularity during those years is attributable to their use of monospaced ( typewriter ) typestyles that allowed computer technology of the time to easily produce the graphics. Modern computers ' superior graphic capabilities have meant these techniques are less often used. A stem - and - leaf display is also called a stemplot, but the latter term often refers to another chart type. A simple stem plot may refer to plotting a matrix of y values onto a common x axis, and identifying the common x value with a vertical line, and the individual y values with symbols on the line. Unlike histograms, stem - and - leaf displays retain the original data to at least two significant digits, and put the data in order, thereby easing the move to order - based inference and non-parametric statistics. A basic stem - and - leaf display contains two columns separated by a vertical line. The left column contains the stems and the right column contains the leaves. Contents 1 Constructing a stem - and - leaf display 2 Usage 3 Notes 4 References Constructing a stem - and - leaf display To construct a stem - and - leaf display, the observations must first be sorted in ascending order : this can be done most easily if working by hand by constructing a draft of the stem - and - leaf display with the leaves unsorted, then sorting the leaves to produce the final stem - and - leaf display. Here is the sorted set of data values that will be used in the following example : 44, 46, 47, 49, 63, 64, 66, 68, 68, 72, 72, 75, 76, 81, 84, 88, 106 Next, it must be determined what the stems will represent and what the leaves will represent. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. In the case of very large numbers, the data values may be rounded to a particular place value ( such as the hundreds place ) that will be used for the leaves. The remaining digits to the left of the rounded place value are used as the stem. In this example, the leaf represents the ones place and the stem will represent the rest of the number ( tens place and higher ). The stem - and - leaf display is drawn with two columns separated by a vertical line. The stems are listed to the left of the vertical line. It is important that each stem is listed only once and that no numbers are skipped, even if it means that some stems have no leaves. The leaves are listed in increasing order in a row to the right of each stem. It is important to note that when there is a repeated number in the data ( such as two 72s ) then the plot must reflect such ( so the plot would look like 7 2 2 5 6 7 when it has the numbers 72 72 75 76 77 ). Stem Leaf 4 4 6 7 9 5 6 3 4 6 8 8 7 2 2 5 6 8 1 4 8 9 10 6 ( displaystyle ( \begin ( array ) ( r l ) ( \text ( Stem ) ) & ( \text ( Leaf ) ) hline 4&4 ~ 6 ~ 7 ~ 9 5& 6&3 ~ 4 ~ 6 ~ 8 ~ 8 7&2 ~ 2 ~ 5 ~ 6 8&1 ~ 4 ~ 8 9& 10&6 end ( array ) ) ) Key : 6 ∣ 3 = 63 ( displaystyle 6 mid 3 = 63 ) Leaf unit : 1.0 Stem unit : 10.0 Rounding may be needed to create a stem - and - leaf display. Based on the following set of data, the stem plot below would be created : - 23.678758, - 12.45, - 3.4, 4.43, 5.5, 5.678, 16.87, 24.7, 56.8 For negative numbers, a negative is placed in front of the stem unit, which is still the value X / 10. Non-integers are rounded. This allowed the stem and leaf plot to retain its shape, even for more complicated data sets. As in this example below : Stem Leaf − 2 4 − 1 2 − 0 3 0 4 6 6 1 7 2 5 3 4 5 7 ( displaystyle ( \begin ( array ) ( r l ) ( \text ( Stem ) ) & ( \text ( Leaf ) ) hline - 2&4 - 1&2 - 0&3 0&4 ~ 6 ~ 6 1&7 2&5 3& 4& 5&7 end ( array ) ) ) Key : − 2 ∣ 4 = − 24 ( displaystyle - 2 mid 4 = - 24 ) Usage Stem - and - leaf displays are useful for displaying the relative density and shape of the data, giving the reader a quick overview of distribution. They retain ( most of ) the raw numerical data, often with perfect integrity. They are also useful for highlighting outliers and finding the mode. However, stem - and - leaf displays are only useful for moderately sized data sets ( around 15 - 150 data points ). With very small data sets a stem - and - leaf displays can be of little use, as a reasonable number of data points are required to establish definitive distribution properties. A dot plot may be better suited for such data. With very large data sets, a stem - and - leaf display will become very cluttered, since each data point must be represented numerically. A box plot or histogram may become more appropriate as the data size increase Notes Jump up ^ Tukey, John W. ( 1977 ). Exploratory Data Analysis ( 1 ed. ). Pearson. ISBN 0 - 201 - 07616 - 0. Jump up ^ For example, MATLAB 's and Matplotlib 's stem functions, do not create a stem - and - leaf display. References Wild, C. and Seber, G. ( 2000 ) Chance Encounters : A First Course in Data Analysis and Inference pp. 49 -- 54 John Wiley and Sons. ISBN 0 - 471 - 32936 - 3 Elliott, Jane ; Catherine Marsh ( 2008 ). Exploring Data : An Introduction to Data Analysis for Social Scientists ( 2nd ed. ). Polity Press. ISBN 0 - 7456 - 2282 - 8. hide Statistics Outline Index hide Descriptive statistics Continuous data Center Mean arithmetic geometric harmonic Median Mode Dispersion Variance Standard deviation Coefficient of variation Percentile Range Interquartile range Shape Central limit theorem Moments Skewness Kurtosis L - moments Count data Index of dispersion Summary tables Grouped data Frequency distribution Contingency table Dependence Pearson product - moment correlation Rank correlation Spearman 's rho Kendall 's tau Partial correlation Scatter plot Graphics Bar chart Biplot Box plot Control chart Correlogram Fan chart Forest plot Histogram Pie chart Q -- Q plot Run chart Scatter plot Stem - and - leaf display Radar chart Data collection Study design Population Statistic Effect size Statistical power Sample size determination Missing data Survey methodology Sampling stratified cluster Standard error Opinion poll Questionnaire Controlled experiments Design control optimal Controlled trial Randomized Random assignment Replication Blocking Interaction Factorial experiment Uncontrolled studies Observational study Natural experiment Quasi-experiment Statistical inference Statistical theory Population Statistic Probability distribution Sampling distribution Order statistic Empirical distribution Density estimation Statistical model L space Parameter location scale shape Parametric family Likelihood ( monotone ) Location -- scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V Optimal decision loss function Efficiency Statistical distance divergence Asymptotics Robustness Frequentist inference Point estimation Estimating equations Maximum likelihood Method of moments M - estimator Minimum distance Unbiased estimators Mean - unbiased minimum - variance Rao -- Blackwellization Lehmann -- Scheffé theorem Median unbiased Plug - in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife Testing hypotheses 1 - & 2 - tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons Parametric tests Likelihood - ratio Wald Score Specific tests Z - test ( normal ) Student 's t - test F - test Goodness of fit Chi - squared G - test Kolmogorov -- Smirnov Anderson -- Darling Lilliefors Jarque -- Bera Normality ( Shapiro -- Wilk ) Likelihood - ratio test Model selection Cross validation AIC BIC Rank statistics Sign Sample median Signed rank ( Wilcoxon ) Hodges -- Lehmann estimator Rank sum ( Mann -- Whitney ) Nonparametric anova 1 - way ( Kruskal -- Wallis ) 2 - way ( Friedman ) Ordered alternative ( Jonckheere -- Terpstra ) Bayesian inference Bayesian probability prior posterior Credible interval Bayes factor Bayesian estimator Maximum posterior estimator Correlation Regression analysis Correlation Pearson product - moment Partial correlation Confounding variable Coefficient of determination Regression analysis Errors and residuals Regression model validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines ( MARS ) Linear regression Simple linear regression Ordinary least squares General linear model Bayesian regression Non-standard predictors Nonlinear regression Nonparametric Semiparametric Isotonic Robust Heteroscedasticity Homoscedasticity Generalized linear model Exponential families Logistic ( Bernoulli ) / Binomial / Poisson regressions Partition of variance Analysis of variance ( ANOVA, anova ) Analysis of covariance Multivariate ANOVA Degrees of freedom Categorical / Multivariate / Time - series / Survival analysis Categorical Cohen 's kappa Contingency table Graphical model Log - linear model McNemar 's test Multivariate Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal Time - series General Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality Specific tests Dickey -- Fuller Johansen Q - statistic ( Ljung -- Box ) Durbin -- Watson Breusch -- Godfrey Time domain Autocorrelation ( ACF ) partial ( PACF ) Cross-correlation ( XCF ) ARMA model ARIMA model ( Box -- Jenkins ) Autoregressive conditional heteroskedasticity ( ARCH ) Vector autoregression ( VAR ) Frequency domain Spectral density estimation Fourier analysis Wavelet Whittle likelihood Survival Survival function Kaplan -- Meier estimator ( product limit ) Proportional hazards models Accelerated failure time ( AFT ) model First hitting time Hazard function Nelson -- Aalen estimator Test Log - rank test Applications Biostatistics Bioinformatics Clinical trials / studies Epidemiology Medical statistics Engineering statistics Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification Social statistics Actuarial science Census Crime statistics Demography Econometrics National accounts Official statistics Population statistics Psychometrics Spatial statistics Cartography Environmental statistics Geographic information system Geostatistics Kriging Portal Commons WikiProject Retrieved from `` https://en.wikipedia.org/w/index.php?title=Stem-and-leaf_display&oldid=864135812 '' Categories : Statistical charts and diagrams Exploratory data analysis Talk Contents Interaction About Wikipedia Deutsch Español Euskara فارسی Français 한국어 日本 語 Norsk Português Русский Tagalog Türkçe Українська 4 more Edit links This page was last edited on 15 October 2018, at 09 : 46 ( UTC ). 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Question: when is a stem and leaf plot used
Answer: for  presenting quantitative data in a graphical format