Central Tendency and Variability
Central Tendency and Variability Sociology 210
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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 (∑(Xx)=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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