Descriptive statistics: describe the data.
   Summarize with statistics (derived, calculated from the data), tabulate (frequency distribution), graph (histogram, etc.)
   Shape. Center. Spread. Outliers.

Data
Qualitative (nominal, categorical) words	Quantitative numbers
	Discrete Continuous integers real nos. (decimals) counts measurements (amount, size, time, rate) how many how much

Levels of measurement

Level (scale)		Examples	What can do with
Nominal	names, labels, categories: (classifying)	[binary/dichotomous]: Yes/No, Agree/Disagree, True/False, Have/Havenot, Success/Failure, M/F, ... MaritalStatus, State, County, Zipcode, Major, Brand,make,model,color, Place race,religion,party,ideology,species,nationality,language, style TaxFilingStatus, Blood type, Housing type, Pet	Count/tally each category. Relative frequency. Mode. Bar chart. Chi-square Tests (independence, goodness-of-fit) Confidence interval 1-PropZInt
Ordinal	orderable/rankable categories but differences (obtained by subtraction) between data values either cannot be determined or are meaningless.	class(frosh/soph/jun/sen), trim levels, film ratings, SML, gold/silver/bronze, letter grades, Education level, clothing sizes, pain scales, military rank, star ratings, priority/risk levels, Mohs Percentiles. Likert scale: Strongly disagree / Disagree / Neutral (or Unsure) / Agree / Strongly agree Very dissatisfied / Dissatisfied / Neutral / Satisfied / Very satisfied Poor / Fair / Good / Very good / Excellent 0/1-10 scales (may be Interval level ↓): pain	Above + median/quartiles, Spearman.
Interval	Numbers: orderable, and differences between data values can be found and are meaningful. But no natural zero (meaning none of the quantity).	Temperature C or F, Years/Dates, shoe size, IQ/SAT (or ordinal ↑), FICO, pH 0 is fakish	histogram mean median SD... Estimation, CI: t-test, Hypothesis testing, ANOVA, correlation & regression
Ratio	Numbers: orderable, and differences between data values can be found and are meaningful, and natural zero (meaning none of the quantity), and ratios (eg. "twice as much") are meanginful.	Weight Height Age Length Area Volume Time Money Energy TemperatureK Angle Information BP LDL FBS BMI    MPG MPH BPM DJI S&P500 counts	Above + CV, GM HM

Measurements have some measuring unit, e.g. inches, pounds, meters, minutes, acres, grams, MPH, BPM, ng/L, ... but they are basically irrelevant for the statistical work.

Data "set" (but can have duplicates) consisting of observations/data values/measurements/datums/individuals/scores of a person, thing or event, all of the same meaning, e.g. weights of adults, greasiness of bags of chips, longevity of bulbs, widget regional sales, effect of pill, number of meal served daily, car make, ...
   Population: complete collection of all the measurements being considered. eg. weights of ALL adults, greasiness of ALL bags of chips
   Sample: a subset of the population.
Whole numbers vs. real (decimal) numbers: no difference calculating stats, histogram, etc.
Negative numbers: ditto. If all negative, "middles" are negative; if some positive, middles might be either or 0. Range and SD always positive.

interval: set of continuous numbers. e.g. [1.45,3.7]    on number line:
OR, where all our data is: [min,max]
range (statistic) is the length or distance of our data interval. Always positive. ↑ 2.25

Some Triola data
Some data distros

Example: Population: weights of adults in country/county.
Not possible to census this. So need a non-biased, representative sample (a teaspoon of the pot of soup).
Ideal: Simple random sample (SRS): every adult equally-likely to be in the sample and every sample of that size is equally-likely.
   The selection procedure/method to take the sample is the "random". Randomly-taken sample.
  Bad: voluntary response, convenience sample.
Collect data. Measured vs self-reported (unreliable).
Calculate/derive statistic from the data: a point estimate of the parameter. But samples have uncertainty/variability so determine [confidence] interval estimate.
Inferential statistics: use probability to understand/quantify/describe uncertainty.
If have census, i.e. population is all known, no need to sample, just describe the population. Sample(s) only useful/taken/needed to estimate population parameter(s).

Data in Text file (.txt, .dat) or webpage, in column (of many columns, each a different data set):
  Open it or Import it in Excel. Select column, copy, then paste into other SW.
    OR
  Open it in Notepad and then select all (Ctrl-A) then copy (Ctrl-C) and paste into Excel. Select column, copy, then paste into other SW.
BodyTemperatures.txt

Stem-and-leaf displays.
   Data: 44 46 47 49 63 64 66 68 68 72 72 75 76 81 84 88 106

			Primes<100	train schedule

Time series chart. temporal measurements. Run chart. Run-sequence plot. Process control chart (statistical quality control).
    
Playfair ~1800
Nightingale 1858
Minard 1869

Boxplot (box-and-whisker plot)

one per sample/experiment. Vertical. Side-by-side comparison. Outliers: ∘

Research papers & technical reports published each day:

Source / Type	Estimated annual output	Per day (approx.)
Peer-reviewed journal articles	3.5 – 5 million	10,000 – 14,000
Conference papers	1 – 1.5 million	3,000 – 4,000
Preprints (arXiv, bioRxiv, SSRN, etc.)	0.6 – 0.8 million	1,600 – 2,200
Technical / government / industry reports	0.5 – 1 million	1,400 – 2,700
Total (all scholarly + technical)	≈ 6 – 8 million	≈ 16,000 – 22,000

Field	% that use statistics	Notes
Biomedical / clinical	90–95%	Almost universal
Psychology / social sciences	85–95%	Very high
Economics / finance	80–90%	High
Biology / life sciences	70–85%	High
Engineering	50–70%	Mixed
Computer science	40–60%	Many theoretical or systems papers have little
Physics / chemistry	40–60%	Theoretical papers often have none
Mathematics / pure theory	5–15%	Mostly proofs
Humanities	5–20%	Low except digital humanities
Overall weighted average	≈ 65–75%	—

So on a typical day, something like 12,000–15,000 new papers and reports appear that contain statistical analysis.

Each pixel randomly black or white:
     Sound track of randomness: