Transcript Colorful Spring Flowers

Chapter 3
Variability
Page 1
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)
Page 2
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
Page 3
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 can’t
have less than zero
variability.
Page 4
Variability: Standard Deviation
Deviation Method: used as a teaching method to help clearly
understand the concept
Formula:
x=X-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
Page 5
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: ΣΧ
-Column 2: square each raw score & then sum the squares: ΣΧ²
-divide the sum of the scores (ΣΧ) by N: M
-divide the sum of the squares (ΣΧ²) 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 don’t find the square root
**The variance is equal to the SD²
•Q:If 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
Page 7
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: R=600 and SD=100
• Leptokurtic distribution: the standard deviation will be LESS than 1/6th
of the range
**EX: R=600 and SD=50
• Platykurtic distribution: the standard deviation will be MORE than
1/6th of the range
Pair Share Topic:
**EX: R=600 and SD=200
What does a standard
deviation tell you?
Page 10