1 Overview of Statistics; Essential VocabularyStatistics: the science of collecting, organizing, analyzing, and interpreting data in order to make decisions

Population and sample

Population: the entire set of individuals of interest

The population is determined by a problem.

Sample: a subset of a population

i.e., members of the population which you actually know something about

Two branches of statistics

Descriptive statistics: organizing, summarizing, and displaying data

Inferential statistics: use of a sample to draw conclusions about a population

To make an inference means to draw a general conclusion about a population from a sample.

Probability is importantly involved in inferential statistics and not at all involved in descriptive statistics.

Variable, Data, Parameter, Statistic

Variable: a characteristic of an individual, to be measured or observed

E.g., if the individuals are people, variables might be height, eye color, ...

Data: information from counting, measuring, or observing

I.e., what you write down about individuals in your sample or population. Note that data point, data value, and data entry allmean the same thing.

Parameter: a value computed from population data

Statistic: a value computed from sample data

A statistic is an estimate of a parameter.

In real life, you hardly ever have a parameter. But we’re interested in parameters (on average, how much does a baby weigh atbirth?), and we use statistics to estimate them, so we need words to distinguish the two.

E.g. Jake measured the diameters of 100 ball bearings chosen from a shipment of 10,000. The average diameterwas 1.1 mm.

Population: the 10,000 bearingsSample: the 100 bearingsVariable: diameterData: Jake’s measured diametersStatistic: 1.1 mm

A statistic changes when the sample changes.

E.g. A 2009 survey of 218 law firms with at least 50 lawyers found that 69% of firms had cut personnel in theprevious year. Is the 69% a parameter or a statistic?

It’s a statistic. In this course, we regard all survey results as statistics. This is because (i) you can rarely contactevery member of the population, and (ii) even if you do, some of them won’t respond.

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Experiment

Another basic term: An experiment is any activity with measurable outcomes, e.g., rolling a die, drawing a card, or med-icating patients. Each possible result of an experiment is called an outcome. An experiment must have an outcome—i.e.,we do not allow “no outcome” as a possibility.

Qualitative and quantitative data

Two basic types of data:

quantitative (or numerical): numbers that are the results of measuring or counting

It makes sense to do arithmetic on quantitative data. It usually makes sense to average it.

qualitative (or categorical): everything elseIt does not make sense to do arithmetic on qualitative data.

E.g. Qual or quant?

(a) diameters of Eastern White Pines: quantitative—these are measured distances

(b) eye color: qualitative

(c) numbers on jerseys of starting team: qualitative (even though they’re numbers, they’re not the resultof counting or measuring

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Hey, girls: here’s what my grandaunt Margaret was up to in 1931:

That’s the Proceedings of the National Academy of Sciences, ladies. Get your Margaret Hilferty on!

Corwin STAT 200©2011-2020 Stephen Corwin

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