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Variability

Topic Review on "Title":

Key Formulas

  • IQR = Q3 – Q1
  • s2 = (1 / (n-1)) ∑(xi– x)2
  • s = √s2

Variables Used

  • Q1= 1st quartile
  • Q3 = 3rd quartile
  • M = Median
  • s2 = variance
  • s = standard deviation

Q1 and Q3

  • To find 1st and 3rd quartiles: 
    • Order the data, find n and median.
    • Divide the data in half.
    • Find the position of the middle value of each half.
    • Determine the value represented by each middle position.

Five Number Summary

  • To find the five number summary:
    • Order the data, find n and median.
    • Find the 1st and 3rd quartiles.
    • Order the five number summary according the symbols: Minimum Q1 M Q3 Maximum

Standard Deviation

  • When calculating the standard deviation, use a table to keep data separated and ordered.
  • First, find the mean of the data set.
  • Second, find the deviation from the mean of each observation.
  • Third, square the deviations.
  • Fourth, take the sum of the deviation squares.
  • Fifth, find the variance.
  • Sixth, take square root of variance to get standard deviation.

Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

This tutorial describes what variability is and its properties. We will show you how to use specific measures of spread to interpret distributions, calculate and interpret quartiles, make a five number summary of data, construct a box plot of five number summary and calculate the standard deviation of a distribution.

After we use the five number summary to make a box plot we will then know how to identify outliers that will greatly affect the variability of the distribution.


Tutorial Features:

Specific Tutorial Features:

  • Step by step examples are shown to introduce variability. Examples as to how to interpret distributions, calculate and interpret quartiles are detailed in the tutorial.
  • Details as to how to make a five number summary of data, construct a box plot of five number summary and calculate the standard deviation of a distribution are also presented with proper example in this tutorial.

Series Features:

  • Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  • Definition slides introduce terms as they are needed.
  • Visual representation of concepts
  • Animated examples—worked out step by step
  • A concise summary is given at the conclusion of the tutorial.

"Title" Topic List:
  • Variability
  • Quartiles
  • Q1
  • Q3
  • Five number summary
  • Boxplot
  • Interquartile range
  • Variance
  • Standard deviation


See all 24 lessons in Introductory Statistics, including concept tutorials, problem drills and cheat sheets:
Teach Yourself Introductory Statistics Visually in 24 Hours

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