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# Psyc 210 Week 3 Notes: Variability 210

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This 5 page Class Notes was uploaded by Victoria Snow on Wednesday September 14, 2016. The Class Notes belongs to 210 at University of North Carolina at Chapel Hill taught by Dr. Harrison in Fall 2016. Since its upload, it has received 16 views. For similar materials see Statistical Principles of Psychology in PSYC at University of North Carolina at Chapel Hill.

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Date Created: 09/14/16

PSYC 210 Week 3 Characteristics of Distributions 9/7/16 Central Tendency- single number descriptors, most common way of describing sample data -describe by its most common/central/typical response -most common=mean -mean=xx̄=x bar Mean=average - Mean means: - Kinda like the midpoint in a seesaw that balances the distribution - Good single descriptor - Even better when comparing groups - “unbiased” estimator of the population: μ (“mew”) - Very useful -The sum of the deviations from the mean will always equal 0. N (X 0 X ) i i1 Mean minimizes deviations Median- point that splits the median in half - Good to use when you have extreme outliers - With odd numbers, middle data point - With even numbers, average of 2 middle points - Good when you have skewed data Problem- interval data - Means and medians really only make sense with interval data The mode is the best/only thing to use with nominal/ordinal data - Most frequent response - Works for all measurement data Marijuana example: mean and median-not helpful Mode: 3. Helpful because most people are “3”=want medicinal use only Ex: 1) mode=3. Med=3. Mean=3 2) mode=3. Med=3. Mean=3.875 3) mode=3. Med=3.5. Mean=5.33 ** Mean gets pulled by outliers** Variability 9/9/16 Variability- difference from central tendency Range= max-min Variance= avg. standard deviation from the mean Standard deviation= square-root of the average squared deviation from the mean n Xi 2 X ) 2 i1 s n 1 2 s = variance; sum of the squared deviations from the mean divided by n-1 (sample size-1) n 2 (Xi X ) i1 s n 1 s = standard deviation; the square root of the variance. Puts scores back into normal scale units. n n n i2 ( XX ) i 2 2 i1 i 1 s n( n) 1 s 2 s Standard deviation in example: people differ from the average in the sample 1 less than in sample 2. (We know this because the standard deviation is less in sample 1 than in sample 2) -mean (central tendency) ~ best guess -variance/variability ~ how good of a guess the best guess is. (if std deviation is 0, then that is BEST guess…the higher the variance, the more “off” the mean is) -Statistics describes aspects of sample -often also interested in the population from which the sample came from -Statistics= “estimators” of aspects of population Sample statistics- for a sample Parameters- for a populations- use greek letters The same words (mean, etc.) mean the same thing and the formulas are the same for sample and population stats. Quantity Symbol Read as Formula Mean X bar n X X i i1 n Variance s2 s-squared n 2 (X i X ) i1 n 1 n X i i1 Standard s s n 2 Deviation (X i X ) i1 n 1 *Use term as “statistic” mostly as blanket term because we are usually estimating*

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