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Type of statistics
In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as
Summary_statistics
Set of descriptive statistics
The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles:
Five-number_summary
Type of statistics
sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the
Descriptive_statistics
Reciprocal of the statistical variance
variance, p = 1 σ 2 {\displaystyle p={\frac {1}{\sigma ^{2}}}} . Other summary statistics of statistical dispersion also called precision (or imprecision) include
Precision_(statistics)
descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary. There are
Seven-number_summary
Value that appears most often in a set of data
Mathematics portal Arg max Central tendency Descriptive statistics Moment (mathematics) Summary statistics Unimodal function Damodar N. Gujarati. Essentials
Mode_(statistics)
Statistic measuring inter-rater agreement for categorical items
describe the relationship between the categories more clearly than a single summary statistic. When predictive accuracy is the goal, researchers can more easily
Cohen's_kappa
Greatest and least values in a statistical data sample
They are basic summary statistics, used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated
Sample_maximum_and_minimum
Difference between a variable's observed value and a reference value
In a given sample, there are as many deviations as sample points. Summary statistics can be derived from a set of deviations, such as the standard deviation
Deviation_(statistics)
Inventory of the global conservation status of biological species
"IUCN Red List of Threatened Species Summary Statistics". IUCN Red List of Threatened Species Summary Statistics. 21 June 2024. Retrieved 21 June 2024
IUCN_Red_List
Kth smallest value in a statistical sample
In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Given a sample of size n {\displaystyle n} , the kth
Order_statistic
Statistic which divides data into four same-sized parts for analysis
quartiles described above provide a five-number summary of the data. This summary is important in statistics because it provides information about both the
Quartile
Number taken as representative of a list of numbers
perhaps not an average, the τ {\displaystyle \tau } th quantile (another summary statistic that generalizes the median) can similarly be expressed as a
Average
Statistical genetics technique
confounding factors, such as population stratification, based on summary statistics from genome-wide association studies (GWASs). The approach involves
Linkage disequilibrium score regression
Linkage_disequilibrium_score_regression
Test used in the analysis of stratified or matched categorical data
In statistics, the Cochran–Mantel–Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data. It allows an investigator
Cochran–Mantel–Haenszel statistics
Cochran–Mantel–Haenszel_statistics
Concept in statistics
In descriptive statistics, the range of a set of data is the size or width of the narrowest interval which contains all the data. It is calculated as the
Range_(statistics)
Study of collection and analysis of data
descriptive statistics. Two elementary summaries of data, singularly called a statistic, are the mean and dispersion. Whereas inferential statistics interprets
Statistics
Middle quantile of a data set or probability distribution
robust approximation to the mean, the median is a popular summary statistic in descriptive statistics. In this context, there are several choices for a measure
Median
Statistic which divides a data set into 100 parts and analyzes it as a percentage
weighted median. Mathematics portal Decile Percentile rank Quantile Summary statistics The typical definition based on greater-than may be called exclusive
Percentile
Statistical measure of association
In statistics, Cramér's V (sometimes referred to as Cramér's phi and denoted as φc) is a measure of association between two nominal variables, giving a
Cramér's_V
Computational method in Bayesian statistics
necessary to identify useful low-dimensional summary statistics. The use of a set of poorly chosen summary statistics will often lead to inflated credible intervals
Approximate Bayesian computation
Approximate_Bayesian_computation
Statistical value representing the center or average of a distribution
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution. Colloquially, measures
Central_tendency
Four data sets with the same descriptive statistics, yet very different distributions
outline of a dinosaur, plus twelve other datasets that have the same summary statistics. Exploratory data analysis Goodness of fit Regression validation Simpson's
Anscombe's_quartet
23-10-0057-01 Railway industry summary statistics on freight and passenger transportation". Statistics Canada. Statistics Canada. 15 May 2026. Retrieved
List of countries by rail usage
List_of_countries_by_rail_usage
Statistical property quantifying how much a collection of data is spread out
Qualitative variation Measurement uncertainty Precision (statistics) Robust measures of scale Summary statistics NIST/SEMATECH e-Handbook of Statistical Methods
Statistical_dispersion
Numeric quantity representing the center of a collection of numbers
tendency Median Mode Descriptive statistics Kurtosis Law of averages Mean value theorem Moment (mathematics) Summary statistics Taylor's law Pronounced "x bar"
Mean
Data combined from several measurements
In statistics, aggregate data are data combined from several measurements. When data is aggregated, groups of observations are replaced with summary statistics
Aggregate_data
Condition in which the value of a measurement or observation is only partially known
reliability oriented) can conduct a maximum likelihood estimation for summary statistics, confidence intervals, etc. One of the earliest attempts to analyse
Censoring_(statistics)
Concept in statistics
In statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter x 0 {\displaystyle x_{0}} , which determines
Location_parameter
Theory in cognitive neuroscience
mind. Ensemble coding proposes that such information is recorded via summary statistics, particularly the average or variance. Experimental evidence tends
Ensemble_coding
Notion in statistics
statisticians compress the information-matrix using real-valued summary statistics; being real-valued functions, these "information criteria" can be
Fisher_information
Statistical method of dividing data into equal-sized intervals for analysis
function Quantile normalization Quantile regression Quantization Summary statistics Tolerance interval ("confidence intervals for the pth quantile") Bagui
Quantile
In statistics, the term higher-order statistics (HOS) refers to functions which use the third or higher power of a sample, as opposed to more conventional
Higher-order_statistics
Public school in Quispamsis, New Brunswick, Canada
55. "Summary Statistics 2015-2016" (PDF). p. 55. "Summary Statistics 2016-2017" (PDF). p. 55. "Summary Statistics 2017-2018" (PDF). p. 53. "Summary Statistics
Kennebecasis Valley High School
Kennebecasis_Valley_High_School
Unit described by the data that one analyzes, in statistics
context of statistical graphics, measured values for individuals or summary statistics for different subpopulations are displayed as separate symbols within
Unit_of_observation
Quantile dividing data into 10 equal parts
normality test. Summary statistics Socio-economic decile (for New Zealand schools) Lockhart, Robert S. (1998), Introduction to Statistics and Data Analysis:
Decile
Town in Tasmania, Australia
locations: Summary Statistics Miena Dam". Australian Bureau of Meteorology. Retrieved 27 January 2016. "Climate statistics for Australian locations: Summary Statistics
Liawenee
Statistic of a given score
In statistics, the percentile rank (PR) of a given score is the percentage of scores in its frequency distribution that are less than that score. Its mathematical
Percentile_rank
Statistical sequence characterizing probability distributions
L-moments as summary statistics in extreme value theory (EVT). This application shows the limited robustness of L-moments, i.e. L-statistics are not resistant
L-moment
original on March 7, 2010. Retrieved April 5, 2010. "1947 BAA Playoff Summary". Basketball-Reference. Sports Reference LLC. Archived from the original
List of New York Knicks seasons
List_of_New_York_Knicks_seasons
Statistics on rape and other sexual assaults
Statistics on rape and other acts of sexual assault are commonly available in industrialized countries, and have become better documented throughout the
Rape_statistics
Statistic used in statistical hypothesis testing
typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform
Test_statistic
Statistical test
from the grand sums, not from group means and variances. Given the summary statistics, the calculations of the hypothesis test are shown in tabular form
One-way_analysis_of_variance
Encyclopedic list of scientific plant names
Online". www.missouribotanicalgarden.org. Retrieved October 18, 2019. "Summary Statistics". The Plant List. Retrieved June 27, 2014. "US, British scientists
The_Plant_List
Collection of statistical data sets
Anscombe's quartet that was created in 1973. The following table contains summary statistics for all thirteen data sets. The thirteen data sets were labeled as
Datasaurus_dozen
DNA base variants frequency distribution
multiallelic frequency spectra exist. Many summary statistics of observed genetic variation are themselves summaries of the allele frequency spectrum, including
Allele_frequency_spectrum
Measures of the characteristics of, or changes to, a population
that is key to making sound decisions about national policy. A useful summary of such data is the population pyramid. It provides data about the sex
Demographic_statistics
By-census – Summary Results" (PDF). Archived (PDF) from the original on 19 October 2019. Retrieved 26 December 2019. Census and Statistics Ordinance 2001
Population census in Hong Kong
Population_census_in_Hong_Kong
Fehérvár 2024–25 football season
Sport. 3 August 2024. "Statistics: NB I, Round 2, Fehérvár vs Diósgyőr – Sofascore". sofascore.com. Sofascore. 3 August 2024. "Summary: NB I, Round 2, Fehérvár
2024–25_Fehérvár_FC_season
Free and open-source statistical program
Analysis, MMIC Model, Latent Growth). Summary statistics: Apply common Bayesian tests from frequentist summary statistics for t-test, regression, and binomial
JASP
Airport serving Green Bay, Wisconsin, USA
International (GRB) Summary Statistics". www.transtats.bts.gov. Retrieved June 12, 2026. "Appleton International (ATW) Summary Statistics". Retrieved August
Green Bay–Austin Straubel International Airport
Green_Bay–Austin_Straubel_International_Airport
is expanded into ungenotyped SNPs and the overlap with public GWAS summary statistics used to estimate risk. The data is then subjected to analysis scripts
Impute.me
Method of plotting numeric data
if the number of samples is not too high. While a box plot shows a summary statistics such as median and interquartile ranges, the violin plot shows the
Violin_plot
JACKSONVILLE INTERNATIONAL AIRPORT TRAFFIC SUMMARY REPORT (PDF) (Report). December 2023. "ONT 2025 End of Year Statistics" (PDF). flyontario.com. Retrieved January
List of the busiest airports in the United States
List_of_the_busiest_airports_in_the_United_States
Results about asymptotic posterior normality
property even with an infinite countable probability space. Different summary statistics such as the mode and mean may behave differently in the posterior
Bernstein–von_Mises_theorem
Theory of statistics
sample of data. Thus the problems theoretical statistics considers include: Choosing summary statistics to describe a sample Summarising probability distributions
Statistical_theory
Statistical method
aggregating Bootstrapping Empirical likelihood Imputation (statistics) Reliability (statistics) Reproducibility Resampling Horowitz JL (2019). "Bootstrap
Bootstrapping_(statistics)
the mathematical basis for several correlation coefficients. The summary statistics is particularly useful and popular when used to evaluate models where
Proportionate reduction of error
Proportionate_reduction_of_error
In statistics, an L-statistic is a statistic (function of a data set) that is a linear combination of order statistics; the "L" is for "linear". These
L-statistic
Town in South Australia
Australia. Retrieved 26 January 2018. "Monthly climate statistics: Summary statistics Summary statistics Port Augusta Power Station (nearest weather station)"
Wilmington,_South_Australia
Data visualization
S. (2010). "The shifting boxplot. A box plot based on essential summary statistics around the mean". International Journal of Psychological Research
Box_plot
Theory and paradigm of statistics
visual summaries. Bayesian epistemology For a list of mathematical logic notation used in this article Notation in probability and statistics List of
Bayesian_statistics
Statistical software package
next set of commands move onto descriptive statistics. summarize price, detail // Detailed summary statistics for variable price tabulate foreign // One-way
Stata
Practice of teaching statistics
Statistics education is the practice of teaching and learning of statistics, along with the associated scholarly research. Statistics is both a formal
Statistics_education
Team records / Results summary". ESPNcricinfo. Retrieved 10 September 2013. "Records / Pakistan / Test matches / Result summary". ESPNcricinfo. Archived
Pakistan national cricket team record by opponent
Pakistan_national_cricket_team_record_by_opponent
and Norwegian-born to immigrant parents". Statistics Norway. "2018 Census ethnic group summaries". Statistics New Zealand. "Tamils in Austria". Tamil Culture
Tamil_population_by_nation
School district in New Brunswick, Canada
located in Miramichi. List of school districts in New Brunswick List of schools in New Brunswick "Summary Statistics 2022-2023" (PDF). gnb. p. 3. [1] v t e
Anglophone North School District
Anglophone_North_School_District
High school in Miramichi, New Brunswick, New Brunswick, Canada
Information " GNB - Department Of Education - Policy & Planning Division: Summary Statistics School Year 2011–2012" MVHS School Website MVHS Official Website v
Miramichi_Valley_High_School
Town in Western Australia
Fitzsimons. p. 109. ISBN 978-0-9581760-0-2. "Summary statistics COOLGARDIE (Site number: 012018)". Climate statistics for Australian locations. Commonwealth
Coolgardie,_Western_Australia
Simultaneous observation and analysis of more than one outcome variable
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e.
Multivariate_statistics
Public school in Salisbury North, South Australia
report" (PDF). decd.sa.gov.au. Retrieved 7 October 2023. "2022 Site Summary Statistics. 0892 - Salisbury High School" (PDF). decd.sa.gov.au. Retrieved 7
Salisbury High School (South Australia)
Salisbury_High_School_(South_Australia)
Statistic for rank correlation
In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of the
Goodman_and_Kruskal's_gamma
The following is a summary of United States presidential elections from 1828 to 2024. Northern Democrats 1860. National Republican Party 1828–32; Whig
United States presidential election summary since 1828
United_States_presidential_election_summary_since_1828
2023. "Population". Statistics Faroe Islands. 10 March 2026. Retrieved 13 June 2026. "The Population and Housing Census Summary". Retrieved 16 July 2024
List of countries and dependencies by population
List_of_countries_and_dependencies_by_population
U.S. Census area of all places with the same ZIP Code
entities developed by the United States Census Bureau for tabulating summary statistics. These were introduced with the Census 2000 and continued with the
ZIP_Code_Tabulation_Area
River in County Laois, Ireland
2019. "Hydrological Data : A listing of water level recorders and summary statistics at selected gauging stations" (PDF). Epa.ie. Retrieved 7 January 2019
River_Erkina
Statistical distribution for dependence between random variables
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each
Copula_(statistics)
High school in Five Rivers, New Brunswick, Canada
Directory " GNB - Department Of Education - Policy & Planning Division: Summary Statistics School Year 2011–2012" "School Profile | Bonar Law Memorial". bonarlaw
Bonar Law Memorial High School
Bonar_Law_Memorial_High_School
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Sadadeen (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
Sadadeen,_Northern_Territory
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Gillen (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
Gillen,_Northern_Territory
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Ciccone(NT)". 2016 Census QuickStats. Retrieved 25 September 2016. "Monthly climate statistics: Summary statistics ALICE
Ciccone,_Northern_Territory
Suburb of Alice Springs, the Northern Territory, Australia
Bureau of Statistics (27 June 2017). "Ross (NT)". 2016 Census QuickStats. Retrieved 27 June 2017. "Monthly climate statistics: Summary statistics ALICE SPRINGS
Ross,_Northern_Territory
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Braitling (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
Braitling
Metric used for testing NLP models
bigrams between the system and reference summaries. ROUGE-L: Longest Common Subsequence (LCS) based statistics. Longest common subsequence problem takes
ROUGE_(metric)
Union - Football Match Summary - June 18, 1990". ESPN. Retrieved 7 June 2023. "Cameroon vs. Colombia - Football Match Summary - June 23, 1990". ESPN.
FIFA World Cup records and statistics
FIFA_World_Cup_records_and_statistics
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "The Gap (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
The_Gap,_Northern_Territory
Airport in Lajamanu
Aeronautical Chart (archived link) "Summary statistics Lajamanu Airport (nearest weather station)". Climate statistics for Australian locations. Bureau of
Hooker_Creek_Airport
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Ilparpa (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
Ilparpa
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Larapinta (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
Larapinta,_Northern_Territory
Town in South Australia
Postcodes Australia. Retrieved 23 August 2019. "Monthly climate statistics: Summary statistics MOUNT CRAWFORD FOREST HEADQUARTERS (nearest weather station)"
Cambrai,_South_Australia
Town in South Australia
Australia. Retrieved 6 December 2018. "Monthly climate statistics: Summary statistics Summary statistics Meningie (nearest weather station)". Commonwealth
Coonalpyn,_South_Australia
National statistics agency of Finland
Statistics Finland (Finnish: Tilastokeskus [ˈtilɑstoˌkeskus], Swedish: Statistikcentralen) is the national statistical institution in Finland, established
Statistics_Finland
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Stuart (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
Stuart,_Northern_Territory
National agency for ensuring food safety
Administration Review of Fisheries in Oecd Countries 2009: Policies and Summary Statistics. OECD Publishing. 2010. p. 334. ISBN 978-9264079748. Retrieved 5 July
Norwegian Food Safety Authority
Norwegian_Food_Safety_Authority
Type of average of a collection of numbers
mean and covariance Standard deviation Standard error of the mean Summary statistics If NM = a and PM = b. AM = AM of a and b, and radius r = AQ = AG.
Arithmetic_mean
US government agency
to the Senate, at whitehouse.gov "Employment Situation Summary". U.S. Bureau of Labor Statistics. August 1, 2025. Retrieved August 18, 2025. (...) Revisions
Bureau_of_Labor_Statistics
Public school in Dalhousie, New Brunswick, Canada
North School District". asd-n.nbed.nb.ca. Retrieved 19 August 2023. "Summary Statistics 2022-2023" (PDF). Government of New Brunswick. p. 52. Retrieved 18
Dalhousie Regional High School
Dalhousie_Regional_High_School
Suburb of Alice Springs, the Northern Territory, Australia
on 18 March 2019. Retrieved 28 July 2019. "Monthly climate statistics: Summary statistics ALICE SPRINGS AIRPORT (nearest weather station)". Commonwealth
Connellan,_Northern_Territory
Suburb of Alice Springs, the Northern Territory, Australia
of Statistics (27 June 2017). "Undoolya (NT)". 2016 Census QuickStats. Retrieved 25 September 2017. "Monthly climate statistics: Summary statistics ALICE
Undoolya,_Northern_Territory
Town in South Australia
February 2007. SA0058907. Retrieved 6 May 2016. "Monthly climate statistics: Summary statistics ROSEDALE (TURRETFIELD RESEARCH CENTRE)". Commonwealth of Australia
Rosedale,_South_Australia
SUMMARY STATISTICS
SUMMARY STATISTICS
Girl/Female
Arabic, Australian, Hebrew
Under God's Rule
Female
English
English name derived from the vocabulary word, summer, from Old English sumor, SUMMER means "summer," the hot season of the year.
Boy/Male
Hindu, Indian, Traditional
Summary
Surname or Lastname
English and German
English and German : from Middle English sum(m)er, Middle High German sumer ‘summer’, hence a nickname for someone of a warm or sunny disposition, or for someone associated with the season of summer in some other way.English : assimilated variant of Sumner.English : assimilated variant of Sumpter.Irish (Leinster and Munster) : Anglicization (part translation) of Gaelic Ó Samhraidh ‘descendant of Samhradh’, a byname meaning ‘summer’. The Gaelic name is also Anglicized as O’Sawrie, O’Sawra.German : from Middle High German summer ‘woven basket’ and, by extension, a measure of grain; also ‘drum’, hence a metonymic occupational name or nickname from any of these senses.
Girl/Female
Arabic, Australian, British, English, Muslim
Fruit; Gifts
Girl/Female
English American
Born during the summer.
Boy/Male
Tamil
Summary, In brief
Boy/Male
Hindu
Summary, In brief
Boy/Male
Tamil
Summary, In brief
Boy/Male
Hindu
Summary, In brief
Girl/Female
American, Arabic, Australian, British, Chinese, English, Hebrew
The Warmest Season of the Year; Summer Season; Name of the Season; Summer; The Hot Season of the Year
Surname or Lastname
English
English : patronymic from Summer 1.Irish (Sligo) : adopted as an English equivalent of Gaelic Ó Somacháin ‘descendant of Somachán’, a nickname meaning ‘gentle’, ‘innocent’.Americanized form of some like-sounding Ashkenazic Jewish name.
Girl/Female
Arabic, Muslim
The First Lady who Obtained Shahadat in Islam
Boy/Male
Tamil
Summary
Boy/Male
Hindu
Summary
Girl/Female
Muslim/Islamic
The first lady who obtained shahadat in Islam
Girl/Female
Muslim/Islamic
Fruit Gifts
Girl/Female
Muslim
Fruit, Gifts
Boy/Male
Hindu, Indian, Marathi
Summary; Gist
Girl/Female
Muslim
The first lady who obtained Shahadat in Islam
SUMMARY STATISTICS
SUMMARY STATISTICS
Boy/Male
Muslim
Compliments, Happiness
Boy/Male
Hindu, Indian
Who Dispels Darkness; The Sun
Boy/Male
Muslim/Islamic
Peace
Boy/Male
Muslim
Causing victory
Boy/Male
Welsh
Welsh surname.
Girl/Female
Biblical
Fullness.
Boy/Male
Spanish
Savior.
Boy/Male
Hindu, Indian, Marathi
Continuous Extended
Girl/Female
Tamil
Chandrakantha | சஂதà¯à®°à®•ாநà¯à®¤à®¾
The Moon, Moon stone, Wife of the Moon
Girl/Female
Indian, Sanskrit
Beautiful
SUMMARY STATISTICS
SUMMARY STATISTICS
SUMMARY STATISTICS
SUMMARY STATISTICS
SUMMARY STATISTICS
a.
Formed into a sum; summed up; reduced into a narrow compass, or into few words; short; brief; concise; compendious; as, a summary statement of facts.
a.
A general or comprehensive statement; an abridged account; an abstract, abridgment, or compendium, containing the sum or substance of a fuller account.
v. t.
Any summary of principles or opinions professed or adhered to.
n.
A short compend; a summary; a brief statement.
n.
A summary account.
n.
A summary.
v. i.
To pass the summer; to spend the warm season; as, to summer in Switzerland.
n.
See Mummery.
a.
Of or relating to coins or money.
a.
Of or pertaining to summer; like summer; as, a summery day.
n.
A summer. See 2d Summer.
a.
Hence, rapidly performed; quickly executed; as, a summary process; to take summary vengeance.
pl.
of Summary
v. t.
To plow and work in summer, in order to prepare for wheat or other crop; to plow and let lie fallow.
adv.
In a summary manner.
a.
Of or pertaining to the mammae or breasts; as, the mammary arteries and veins.
pl.
of Mummery
a.
Fond of sugar or sweet things; as, a sugary palate.
v. t.
To keep or carry through the summer; to feed during the summer; as, to summer stock.
n.
A compendium; an epitome; a summary.