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Mean, Median, & Mode

by: Amy Turk

Mean, Median, & Mode Psyc-21621

Amy Turk

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Notes on Chapter 3
Quantitative Methods Psych I
Dr. Gordon
Class Notes
Psychology, Stats, Statistics, mean, median, mode, percentile, Rank, central, tendency, mew, sigma
25 ?




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This 3 page Class Notes was uploaded by Amy Turk on Wednesday April 27, 2016. The Class Notes belongs to Psyc-21621 at Kent State University taught by Dr. Gordon in Spring 2016. Since its upload, it has received 14 views. For similar materials see Quantitative Methods Psych I in Psychlogy at Kent State University.


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Date Created: 04/27/16
PSYCH STATS POWERPOINT 3 ● percentile is a score that is used to determine the percentile rank ● central tendency: single score chosen to represent the entire set of scores ○ defines the center of distribution ○ allows you to compare 2 sets of data ● problems… its a single score ○ no standard procedure to calculate ○ not all distributions are the same ■ some aren’t symmetrical and this makes it more difficult to determine the best value to be representative of the sample ● the mean: the average ● median: middle value ● mode: most common value Mode ● calculated by looking at the most common value ● taken straight from the scores ● best used for nominal data ● if two values occur the most: middle modes ○ 1 = unimodal ○ 2 = bimodal ○ 3 or more = multimodal ● can be used with categorical/non numerical data ● always an actual score from the data set ● multiple modes ● describes shape ○ a better indication of the shape of the distribution than the mean alone ● identifies location of the peak in frequency distribution Median ● midpoint score ○ half are above and half are below ● order scores from lowest to highest ● relatively unaffected by extreme scores ● better alternative than the mean when the distribution is skewed ● we don’t care about distance between scores with the median ● useful for ordinal scale as well ○ defined by direction Mean ● the average = the sum of scores divided by the number of scores ○ mew symbol = mean for population ○ X with line on top = sample mean ■ sum of all scores in a sample divided by the sample size ● calculating population mean = sigma X divided by N ● calculating sample mean = sigma X divided by n ● weighted mean ○ use for multiple sets of scores ■ when you have means for different groups but want to know the overall combined mean ○ add scores and divide by the total size ● characteristics of a mean change… ○ when you add a score or remove a score ○ change a score ○ add/subtract/multiply/divide a constant from the score ● changing a score changes the sum of scores ○ changing a score does not change n ● mean moves in the direction of the change ○ not by the same amount as the change ● adding or removing a score ○ changes the sum of scores (sigma X) ○ changes the number of scores (n) ○ the mean moves ● median is a better representative for income ○ ordinal is best for median ● mode is best for categorical data ● adding or removing a score ○ changes the sum of scores ○ changes n… total number of scores ○ the mean moves ■ add = mean moves toward the added score ■ remove = mean moves away from the removed score ■ the only exception is if you add a score equal to the mean ● adding or subtracting a constant ○ the mean will increase by the constant amount if you add a constant ■ if you remove a constant, the mean will get lower by that exact constant ● multiply/divide by a constant ○ typically done when you want to change the scale of measurement ○ if you multiply by a constant, the mean changes by multiplying it by that constant ○ same thing for division ● when you include a constant, it changes the sum of the scores, but not the total number of scores ● the mean is the most preferred method ○ uses every score… most representative ○ closely related to other descriptive stats ● we expect that the different measure of central tendency will usually be the same ○ this isn’t always true ● symmetrical distributions ○ mean and median are always the same ● unimodal: one mode ○ same as mean and median ● bimodal/multimodal ○ multiple modes ● the mode is the highest rank ○ there may not be a mode ■ if all the data is exactly the same ● skewed distributions ○ mode will be located at the peak on one side ■ mean usually will be displaced toward the tail on the other side ○ median is usually between mean and mode ● mean affected by outliers ○ gets pulled in the direction of the outliers ● positively skewed: mode, median, mean ○ mean is farther to the right as influenced by extreme scores at tail ● negatively skewed: mean, median, mode ○ mean is farther to the left ● mode = unaffected by skew ● median = mildly affected by skew ● a skew means that there is at least one outlier ● central tendency is a descriptive statistic ○ used heavily in inferential stats


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