Sept 27
Learning objectives
- List and describe all 5 properties that make mean special, Explain how measures of central tendency change
when the shape of distribution changes, Define and calculate 3 measures of variability, Interpret standard
deviation, Calculate standard deviation using deviation scores and computational formulas, Calculate z-score
using raw score and interpret what it means in terms of standard deviation, Convert raw score to z-score and
back again, List 3 key features of z-scores, Interpret table A (z-scores), Use z-score method to find percentile
rank for particular raw score, Use z-score to find raw score for particular percentile
A. 5 Properties that make the mean special
(i) Sensitive to all scores
a. If a score is changed the mean will always change; every score is used in its calculation
(ii) Very sensitive to extreme scores
a. Median isn’t sensitive to extremes; more appropriate when you have extreme scores
b. Central Tendency and symmetry
c. Ex. If you have severely negative skewed distribution measured on ratio scale, which would be most
appropriate indicator of central tendency to calculate and report? Mean, median, mode, all of the
above.
i. Median
(iii) Its deviation scores add to zero
a. Ex. What is a deviation score?
b.
c. ONLY the mean’s deviation scores add to zero
d.
(iv) Its squared deviation scores, when added, are the smallest you can get
(v) Least sensitive to weird samples when drawing from a population
a. Main reason why we use mean as our primary measure of central tendency when calculating
inferential statistics
b. Studies use samples from population; every time we draw sample, results won’t be exactly the
same i. If relied on median or mode, results would vary wildly
ii. The mean is cool, typically not sensitive to these sampling variations
B. 3 Common Measures of Variability
a. Variability: amount of spread in distribution of scores on a variable
b. Range
i. Crude: only considers 2 most extreme scores
c. Standard deviation
i. Take a set of raw scores for a variable
d. Variance
i. The standard deviation, squared

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