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Psy 202 Chapter 3

by: T'Keyah Jones

Psy 202 Chapter 3 Psy 202

T'Keyah Jones
GPA 3.0

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About this Document

These notes cover Central Tendency and Variability
Elementary Statistics
Dr. Melinda Redding
Class Notes
elementary statistics, Psychology
25 ?




Popular in Elementary Statistics

Popular in Psychology (PSYC)

This 5 page Class Notes was uploaded by T'Keyah Jones on Saturday September 3, 2016. The Class Notes belongs to Psy 202 at University of Mississippi taught by Dr. Melinda Redding in Fall 2016. Since its upload, it has received 7 views. For similar materials see Elementary Statistics in Psychology (PSYC) at University of Mississippi.


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Date Created: 09/03/16
Psy 202 Elementary Statistics  Chapter 3: Measures of Central Tendency and Variability a. Central Tendency A single value used to represent the typical score in a set of scores b. Three Measures of Central Tendency Mean Median Mode c. Mean The average Influenced by outliers Formula: ΣX      N µ Mean of population M Mean of sample Mx                                                                                     My Mean of "X" variable                                                      Mean of "Y" variable d. Median The middle score The mid­point of right distribution Not influenced by outliers Right distribution Scores listed in order If "N" is odd The median is the middle score If "N" is even Find the two middle scores and find midpoint e. Mode Score that occurs the most The peak(s) of a simple frequency distribution There can be more than 1 Center of a normal distribution f. Distributing Shapes Symmetrical Distribution: Uni There is only 1 peak Symmetrical Distribution: Bi There are two peaks Skewed Distribution The mean is pulled toward the tail If the mean is high                        If the mean is low       Positive                                          Negative g. Reporting Central Tendency Nominal data Mode Ordinal data Median Interval/Ratio Data Depends on the shape of the distribution Normal Distribution                                     Skewed/Open­Ended Distribution          Mean                                                                    Median h. Variability Descriptive statistics Refers to the "spread" of scores in a distribution To describe distribution Shape Central Tendency Variability Types Range                                 Variance Interquartile Range            Standard Deviation Range Simplest measure X high X low Disadvantage not very stable because it uses only two scores heavily influenced by outliers Interquartile Range Uses only the middle 50% of the score X high X low   the middle 50% distribution Good for skewed distribution Population V. Sample The variability within a population is greater than the variability within a sample Variability statistics will always underestimate variability parameter (biased estimate) When calculating variance and standard deviation on a sample, a correction is made in the  formula to yield an "unbiased estimate" of the population variance Unbiased estimate For variance Using a corrector factor for a more accurate answer i. Variance Uses all scores The average of squared deviations from the mean 1.  Find the deviation scores (X­µ) or (X­M) 2. Square the deviation scores 3. Sum the square deviation scores 4. find the average of squared deviation scores Advantage Uses all scores Not heavily influenced by outliers Disadvantage Difficult to interpret squared units Scores that are similar                                       Scores that are different Little variability (spread)                                   Large variability (spread) j. Standard Deviation How much do the scores deviate from the mean on average Easier to interpret than variance because it is in the same units as the original data 1. Find the variance 2. Take the square root of the variance k. Variance (Definitional Formulas) Variance population                                     Variance sample           o                                                                       s 2  2                                           2                        2 o =  Σ(X­µ)   s  =  Σ(X­M)               N                                                                    N­1 SS Sum of squares Example Population data set: 12,9,15,13,11 N = 5 M = 12 2  X     X ­ µ (deviation score)      (X ­ µ) 12                  0          0 9                 ­3          9 15                  3          9 13                  1          1 11                 ­1          1                                                           Σ(X ­ µ)  = 20 2  o = 20 = 4.00            Standard Deviation: 2.00          5 s = 20 = 5.00            Standard Deviation: 2.24         4 l. Variance (Computational Formulas) 2  2 2 o = ΣX  ­  (ΣX)          _______N                      N s = ΣX  ­  (ΣX)  2        ______N                  N­1 Example 2      X            X 6.95 48.3025 7.09 50.2681 7.08 50.1264 7.19 51.6961 7.15 51.1225 6.92 47.8864 N = 6 ΣX = 42.38 2  ΣX = 299.40 o = 299.40 ­  (42.38)  2                =        0.01         _________6                           6


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