Colorful Spring Flowers

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Chapter 3 Variability
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Variability

• Central tendency tells us about the similarity
  between scores
• Variability tells us about the differences
  between scores
• -ie. how spread out are the scores in the
  distribution?
• -ie. how close or far from the mean are the
  scores?
• There are 3 measures of variability range,
  standard deviation variance

Measures of Variability Worksheet (In-Class)
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Variability Range

• Symbolized by R
• It is the measurement of the width of the entire
  distribution
• To calculate Subtract the lowest value from the
  highest value
• Least useful measure of variability

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Variability Standard Deviation

• Symbolized as SD
• The average amount that scores in a distribution
  deviate from the mean.
• The most common descriptive statistic for
  variability.
• Two ways to calculate
• -the Deviation Method
• -the Computational Method

Note standard deviations are never less than
zero because you cant have less than zero
variability.
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Variability Standard Deviation
Deviation Method used as a teaching method to
help clearly understand the concept
Formula
xX-M x is the deviation score

• To calculate
• -find the mean
• -subtract the mean of the distribution from
  each score (X-M) or x
• -square each difference (X-M)² or x²
• -sum the squares
• -divide by N
• -take the square root

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Variability Standard Deviation
Computational Method is a shortcut that is used
most often. -this is what you should
use
Formula

• To calculate
• -Column 1 sum the raw scores S?
• -Column 2 square each raw score then sum the
  squares S?²
• -divide the sum of the scores (S?) by N M
• -divide the sum of the squares (S?²) by N
  subtract the squared mean (M²)
• -find the square root

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Variability Variance

• Symbolized by V
• Measure of how spread out a set of scores are
• Average of the squared deviations from the mean
• Also called the mean square deviation
• To calculate V calculate the SD but dont find
  the square root
• The variance is equal to the SD²
• QIf the variance is just the square of the SD,
  why use it?
• -A some formulas require using the
  variance rather than the SD

Formula
Measures of Variability Homework due next class
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Range Percentiles

• Percentile the point on a distribution where a
  given percentage of scores fall below.
• EX 95th percentile means A LOT of
  scores fall below it
• EX 5th percentile means very FEW
  scores fall below it
• -Percentiles are used to show various
  forms of range
• -Note The 50th percentile is right in
  the middle of the distribution so it is always
  equal to the median.
• Quartiles divide a distribution into quarters
• -1st quartile coincides with the 25th
  percentile
• -2nd quartile coincides with the 50th
  percentile
• -3rd quartile coincides with the 75th
  percentile

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Range Percentiles

• Deciles divide a distribution into tenths
• -1st decile is equivalent to the 10th
  percentile so on
• -the lowest score would be in the 1st
  decile the highest score would be in the 10th
  decile
• Interquartile Range find the difference between
  the 1st 3rd quartiles
• -middlemost 50 of the distribution
• Interdecile Range find the difference between
  the 1st 9th deciles
• -middlemost 80 of the distribution

Percentiles Worksheet
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Assessing Kurtosis 1/6th Rule

• Use the 1/6th rule to quickly evaluate the
  kurtosis of any unimodal symmetrical distribution
• Mesokurtic distribution standard deviation is
  approximately 1/6th of the range
• -divide the range by 6 to get the
  approximate standard deviation
• EX R600 and SD100
• Leptokurtic distribution the standard deviation
  will be LESS than 1/6th of the range
• EX R600 and SD50
• Platykurtic distribution the standard deviation
  will be MORE than 1/6th of the range
• EX R600 and SD200

Pair Share Topic What does a standard deviation
tell you?