6.1.2

Statistics Key Terms

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Statistics Key Terms

Statistics is about estimating information about the whole group by using a smaller group.

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Population and sample

  • A whole group is called a population and a smaller group within the population is called a sample.
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Sample needs to be representative

  • When choosing a sample it is important for it to be representative of the whole population so that measurements we take in the sample can be used as estimates for the population.
  • To be representative the sample needs to be big enough to be reliable, and the sample should be random so that every member of the population is equally likely to be chosen.
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Random sample

  • To choose a random sample you can assign a number to each member of the population then use a computer or a random number table or pick numbers out of a hat to choose a random selection of numbers.
  • Pick the members corresponding to these numbers.
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Biased sample

  • A biased sample is one that doesn’t represent the whole population.
  • To assess whether a sample is biased think whether any groups of people would be excluded from the sample (e.g. based on gender, age, different interests or habits).
  • A small sample is also likely to be biased.

Types of Data

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Primary vs secondary

  • Primary data is data that you have collected yourself.
  • Data from any other source (e.g. from a book or the internet) is secondary data.
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Qualitative vs quantitative

  • Qualitative data is descriptive or categorical and uses words rather than numbers (e.g. colours, names).
  • Quantitative data is measured in numbers and represents quantities (e.g. heights, shoe size).
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Discrete vs continuous

  • Quantitative data is discrete if the numbers can only take certain values (e.g. only whole numbers).
  • It is continuous if the numbers can take any value.

Capture-Recapture Method

A capture-recapture method can be used to estimate the population size from a sample.

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Process

  • A sample is captured, tagged and released.
  • Later another sample is taken and the number of tagged members is noted.
  • Using the assumption that the proportion of tagged members in the population is the same as the proportion in the sample you can then estimate the population.
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Example

  • A biologist captures 15 turtles from a lake and marks their shells with paint.
  • The next week they capture 20 turtles and find 5 have their shells marked.
    • 520 = 15N where N is the population size so the estimate is N = 60.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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