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.

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.

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.

• Variability
  
• Quartiles
  
• Q1
  
• Q3
  
• Five number summary
  
• Boxplot
  
• Interquartile range
  
• Variance
  
• Standard deviation