Basic Terminology

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Basic Terminology
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Statistics

• Statistics is the process of
• Collecting data
• Organizing data in tables
• Summarizing data via graphs and calculations
• Analyzing the data
• Interpreting the results

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Descriptive vs Inferential

• Descriptive statistics is primarily steps 1 to 3
  of the previous slide. In Math 123, we do
  primarily descriptive statistics.
• Inferential statistics is primarily steps 4 and 5
  of the previous slide. In Math 123, we do a
  little bit of this with the last 2 lessons on
  confidence intervals and hypothesis testing.

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Population

• A population is the largest group of subjects
  under consideration.
• A parameter is a numerical measure of the
  population.
• Example The population could be all of the
  students who take classes at M.C.C. A parameter
  could be their average age.

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Sample

• A sample is some part of the population.
• A statistic is a numerical measure of the sample.
• Example We could survey 100 students who attend
  M.C.C. for a sample. The average age of those
  100 students would be a statistic.

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CAUTION

• In order for results to be meaningful, the sample
  must be truly representative of the population.
• Example
• If we surveyed only day students, the average age
  might be too low as night students tend to be
  older, working students.

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Variables and data

• A variable is a characteristic or attribute that
  can assume different values.
• Example Heights of people
• Data is the specific value of the variable.
• Example A man is 510 tall.

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Classifying Data

• Data can be classified in 2 major categories
• 1. Qualitative the data consists of
  non-numeric values
• Examples college majors, hair color
• 2. Quantitative the data consists of numeric
  values
• Examples heights, body temperatures

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Continuous and Discrete

• Continuous data is obtained by a measuring
  process.
• Examples car speed, height, temperature
• Discrete data is obtained by a counting process.
• Examples number of students in a class, money

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Four levels of data

• 1. Nominal The data consists just of names or
  labels.
• Examples college majors, hair color, town you
  live in, religion

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• 2. Ordinal There is an implied ranking of the
  data.
• Examples ratings of your professor (excellent,
  good, fair, poor), sizes of cars (full size,
  intermediate, compact)

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• 3. Interval The data can have the values
  subtracted, but division is not meaningful.
• Example Temperature
• We can say that 80o is 40o more than 400,but we
  can not say that 80o is twice as hot as 40o.

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• 4. Ratio The data can be both subtracted and
  divided meaningfully.
• Example Salaries
• We can say that a salary is 150,000 is 100,000
  more than a salary of 50,000. It is also 3
  times as much.

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Ways of obtaining data

• 1. Sampling We survey part of the population.
• 2. Census We survey the entire population.

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• Observational study We observe the subjects but
  we do not attempt to modify the subjects being
  studied.
• Example We observe how many drivers speed on
  the campus.

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• Experiment we apply some sort of treatment and
  observe the effects.
• Example We give 50 subjects a drug to reduce
  blood pressure and observe whether or not it
  works.

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Methods of sampling

• Random Each individual member of the population
  has an equal chance of selection.
• Example We use a computer to generate random
  student identification numbers and then survey
  those students.

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• Systematic Select some starting point and then
  select every kth member of the population.
• Example We survey every 10th student entering
  the library.

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• Cluster Divide the population into groups,
  called clusters. Select a few clusters and
  survey every member of those clusters.
• Example An apartment complex consists of 20
  buildings. Select 4 of the buildings and then
  survey residents of every apartment within those
  4 buildings.

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• Stratified Divide the population into 2 or more
  groups. Survey an equal number from each group.
• Example Survey 50 full time students and 50
  part time students to determine the average
  number of hours each group works.

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• Convenience Use results that are easy to
  obtain.
• Example To do a statistics project on number of
  hours that students work, you ask students in
  your English and history classes.