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Central Tendency and Variability

by: Kaiyana Dudley

Central Tendency and Variability Sociology 210

Marketplace > University of Michigan > Statistics > Sociology 210 > Central Tendency and Variability
Kaiyana Dudley


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About this Document

Simple intro to central tendency and variability
Elementary Statistics
Jennifer Barber
Class Notes
Math, Statistics, variance, standard deviation
25 ?




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This 2 page Class Notes was uploaded by Kaiyana Dudley on Saturday September 17, 2016. The Class Notes belongs to Sociology 210 at University of Michigan taught by Jennifer Barber in Fall 2016. Since its upload, it has received 7 views. For similar materials see Elementary Statistics in Statistics at University of Michigan.


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Date Created: 09/17/16
● Wha ​ t is central ​ ncy?  ○ The textbook definition words it as a statistical measure that attempts to determine  the single value that is most typical or most representative of the entire set of scores  ○ A simpler definition: the center of most common number of a distribution  ● What does central tendency look like?  ○ The central tendency is usually understood as the mean, median, or mode  ■ The ​mean​ is the center of gravity or the average out of all the scores  ■ You can find the mean by simply adding up all of the numbers in the  distribution and dividing by the number of scores  ■ Algebraically, the population (or distribution) mean can be written  using summations (∑) or  μ, and the sample mean is represented by  X­bar () ̄ ■ The ​median​ can be found by putting all of the scores in order and locating the  center value  ■ If there are two center values, add them together and dividing by 2  ■ The ​mode ​ is the score that shows up most frequently  ■ There can be no mode or more than one if certain scores are similarly  common  ● How do I know which measure will represent the central tendency best?  ○ It's not always obvious which measure to use, but here are a few  key indicators to  remember  ■ When there are extreme outliers, it may be best to use the  median or mode  ■ The mode won't explain central tendency unless it is very dominant  ■ The median is less sensitive than the mean to extreme values  ● What is variability?  ○ Variability ​shows the differences between scores in a population that describes  whether scores are spread out or clustered together around the center of distribution  ■ This can also be referred to as the ​measure of dispersion  ■ The range, interquartile range, or semi­interquartile range are based  on the distance between scores of different rank  ■ The ​variance ​and ​deviation ​are measures based on the distance of a  score (or group of scores) to the center of the distribution  ○ Variability basically tells us how well a score(s) represent the entire population  ● Can you explain more about the measures of variability?  ○ The ​range​ is the difference between the highest (upper real limit) and lowest (lower  real limit) score of the entire distribution  ● Where does the quartile stuff come in?  ○ We mark the quartiles when the scores are ranked in ascending order  ○ A distribution can be split up in four quartiles (Q1, Q2, Q3, & Q4)  ■ A ​percentile​ is a value on a 1­100 number scale of the distribution that tells  the percentage of a score  ○ Q1 is the first quartile that represents 25th percentile  ■ Q2=50%, Q3=75%, and Q4=100%  ○ The ​interquartile range​ is the difference between Q3 and Q1 (Q3­Q1)  ■ The semi­interquartile range is ((Q3­Q1)/2)  ● What about deviation and variance?  ○ Deviation ​is a score's distance from the mean (X­μ)  ○ The average of the deviation scores will always equal zero (∑(X­​x)=0)  ■ This is the population ​variance​ that is the average squared distance from the  mean (but this isn't what we want because it equals zero)  ■ It equals the mean squared deviation  ■ For statistics, our goal is to measure the variability by finding the  standard deviation ​from the mean, which is the square root of  variance             References  Essentials of Statistics for the Behavioral Sciences by Frederick J Gravetter, Larry B. Wallnau, Chapter 2­4  Jennifer Barber Lecture 2 Slide Presentation (September 13 &15, 2016)   


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