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Central Tendency
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AVERAGE a statistical meausre to determine a single score that defines the center of a distribution. the goal of central tendency is to find the single score that is most typical or most representative of the entire group.
The average vaule can then be used to provide a simple description of the entire population or sample. - good also for making comparisons.
Describe a large set of data with a single, representative number.
NO single measure will always produce a central, representative value in every situation.
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Mean - central tendency measurment
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ARITHMETIC AVERAGE: for a distribution is the sum of the scores divided by the number of scores.
Sum all the scores then divide by the N
Mean for a sample is identifed by M or x-bar.
Population Mean - Mew=MX/N
Sample Mean - x-bar = MX/n
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Median - central tendency measurement
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The score that divides a distribution in half so that 50% of the individuals in the distribution have scores at or below the median
Determine the midpoint
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Mode - central tendency measurment
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FASHIONABLE: distribution, the mode is the score or category that has the greatest frequency
Useful measure of central tendency because it can be used to determine the typical or average value for any scale of measurment, including a nominal scale
ex. a restaurant name
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Extreme skewed distributions
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When are a few extreme scores, the mean may not be a good representative of the majority of the distribution. they can have too much influence and cause the mean to be displaced- because it uses all the scores equally. SO the median is used when reporting the average value for a skewed distribution
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What happens if there are undetermined values. ex: if someone does not complete a test that is based on time because they couldn't figure out how to do the puzzle?
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It is impossible to compute the mean for this data because of the undetermined value. it IS possible to compute the median...in the middle, the score...including the data "Never finished"
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Open ended distribution
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A distribution is said to be open ended when there is NO UPPER LIMIT for one of the categories - of 20 families.
ex. "5 or more children" - open ended category....you can't find the total number of children for all 20 families.
Can find the MEDIAN! Not the mean.
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Is the mean appropriate to describe central tendency for ordinal data?
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The MEDIAN is always appropriate - when measured on a ordinal scale.
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When do you use the mode? (3 common situations)
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1. Nominal scale - nominal scales, do not measure quantity...cannot do median or mean. MODE is only option.
2. Discrete variable - exist only in whole indivisible categories. ex. # of children....the computing means will generate results such as the ave family has 2.4 children. Mode, always identifies the most fashionable case., it produces the more sensible measures of central tendency.
3. Describing shape - mode requires no calculations
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Are modes shown in graphs?
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No
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What do graphs do?
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Show the relationsihp between two variables
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Bar graph rules
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1. the height of a graph should be apprx. 2/3 of its length
2. start numbering both X and Y axis' with zero.can do intersection...
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Central tendency - which 3 are used for a single set of data?
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Mode, mean, median
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Symmetrical distribution
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Right side will mirror left side of graph. median will be exactly at the center of a symmetrical distribution, mean also. FOR ANY SYMMETRICAL DISTRIBUTION, THE MEAN AND MEDIAN WILL BE THE SAME! If it has only one mode...it will also be the same.
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Bimodal distribution
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2 or more modes...same fashionable numbers.
if the bimodal distribution is symmetrical, it will have the mean and median in the middle of it.
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