Math 175 Elementary Statistics Online Class Notes & DO IT NOW Problems

Module 1 Introduction to Statistics, Part I

Definitions:

Statistics is the process that begins with the collection of data (after carefully designing a collection

protocol) and that ends with conclusions, predictions, or summarization of trends.

A variable is a characteristic of a group of objects that is well-defined and that varies among those objects.

Examples: Age, Height, Number of siblings, Relationship Status, Zip Code

A sample is a subset of a population used to make estimations about the population.

Sampling is the process of selecting a sample.

Classifications of statistics and variables:

Descriptive Statistics make summarizations about a group of data

Inferential Statistics make estimations about population variables or predictions.

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(1) Identify each of these statements as descriptive or inferential.

1-1.1: The average number of beers consumed by Steelers tailgaters before kickoff is 4.3.

1-1.2: The projected fuel efficiency for American made cars by 2020 will be 36.5 mpg.

1-2.3: The class average for the Final Exam was 72.8%.

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Qualitative Variables have non-numerical, or arbitrarily assigned numerical values.

Examples: Make of car, zip code, ID number, home state

Quantitative Variables have meaningful numerical values.

Examples: Age, number of siblings

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(2) Identify each of these variables as qualitative or quantitative.

1-2.1: Letter Grade

(A F)

1-2.2: Bathtub capacity

(gallons)

1-2.3: Relationship Status

1-2.4: Shoe Size

1-2.5: Class standing

(Fr/So/Jr/Sr)

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A Discrete Variable has values that can be counted. All qualitative variables are discrete.

Examples: Number of siblings, make of car, rank (1st, 2nd, 3rd, . . .)

A Continuous Variable has values that come from a continuum, or continuous range of numerical values

Examples: Elapsed time, salary, weight

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(3) Identify each of these variables as discrete or continuous.

1-3.1: Letter Grade

(A F)

1-3.2: Bathtub capacity

(gallons)

1-3.3: Relationship Status

1-3.4: Shoe Size

1-3.5: Class standing

(Fr/So/Jr/Sr)

Math 175 Elementary Statistics Online Class Notes & DO IT NOW Problems

Module 1 Introduction to Statistics, Part I

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The values of a variable with nominal level of measurement can be grouped into categories which have no inherent

order.

Example: Relationship status

The values of a variable with ordinal level of measurement can be grouped into categories which have an inherent

order.

Example: Movie ratings

The values of a variable with interval level of measurement can be comparatively ranked and zero is a value that

does not correspond to a lack of the variable.

Example: Temperature

The values of a variable with ratio level of measurement can be comparatively ranked and zero is a value that

corresponds to a lack of the variable.

Examples: Salary, Number of siblings

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(4) Identify the level of measurement for each variable below nominal, ordinal, interval or ratio.

1-4.1: Letter Grade

(A F)

1-4.2: Bathtub capacity

(gallons)

1-4.3: Relationship Status

1-4.4: Shoe Size

1-4.5: Class standing

(Fr/So/Jr/Sr)

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(5) What are the four variables in the study description below? Determine whether each is

quantitative or qualitative; discrete or continuous; and the level of measurement.

In order to determine how several small local streams react to a variety of

weather conditions, researchers collected data at twelve different sites over the

past year. Among those data, the researchers took daily readings of the amount

of rain (in inches) that had fallen in the past 24 hours, and the flow of the

streams (in cubic feet per second) at a specific time each day. Reference

materials available provided the research team with an ecological health grade

for each stream (from A down to F) and the streams order, which is the

number of streams that feed into it (values range from 0 to 11). Conclusions are

expected to assist in the planning of development along local streams and in the

restoration of other similar streams