Chapter 3 & 4

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measures of central tendency such as ________________________________ summarize a distribution of scores by describing the most common, the middle score, or the average score of the distribution

mode, median, and mean

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central purpose of descriptive statistics is to __________________ data

summarize or reduce

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always the exact center of a distribution of scores

mode

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median can be found for _______________ data, but generally it more appropriate for ______________ data.

interval ratio; ordinal

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______________identifies a point below which a specific percentage of cases fall

percentile

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the 5th decile, is equal to the ________ percentile

50th

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D1 or the first decile is the point below which ______________ of the cases fall

10%

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If you scored higher than the 3rd quartile (Q3) then you made __________________________

above 75% of the scores

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most commonly used measure of central tendency

mean (x bar)

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formula for mean (x bar)=

the sum of (xi) / N

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three characteristics of the mean:

1. the mean balances out all scores (mean is pt around which all scores cancel out); 2. mean minimizes variation of scores (least squares principle); 3. mean affected by all scores and can be misleading if distribution has extreme outliers

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what does least square principle say?

mean is pt around which variation of score is minimized; if difference b/t scores and mean are squared and then added, the resultant sum will be less than the sum of the squared differences b/t the scores and any other point in the distribution

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This principle underlies the fact that the mean is closer to all of the scores than the other measures of central tendency

least squares principle

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distributions with outliers have a ___________:

skew

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if you have some extremely high outliers, what will happen to the distribution curve?

it will skew to the right (+) = (mean>median)

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when mean > median, what would you expect your distribution curve to look like?

skewed to the right (+ skew)

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if you have some extremely low outliers, what will happen to the distribution curve?

it will skew to the L (-) = mean< median

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if mean < median, what would you expect your distribution curve to look like?

skewed to the left (- skew)

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the mean will be pulled _______________ of the outlying scores relative to the median

in the direction

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the greater the skew, the ______________ the difference between the 2 measures of central tendency (mean & median)

greater

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the mean and median will have the same value only in distributions that are ________________-

symmetrical

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the mode is the most ___________________ and is used most appropriately with _____________________variables

common value; nominal-level

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_____________ describe the variety, diversity, or heterogeneity of a distribution of scores; describes the variability of data (variants.)

measures of dispersion

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measure of dispersion can reveal substantial differences between distributions even when _____________________ are the same

measures of central tendency

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range:

distance between highest and lowest scores in distribution (high score-low score)

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the greater the value of a range the greater the _______________ in the distribution

dispersion

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limitations to range

range might exaggerate the amount of dispersion for most of scores in distribution

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IQR:

the distance from the third to 1st quartile; a kind of range that acoids some of the problems associated with range outliers by considering only the middle 50% of the cases in distribution

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three traits a good measure of dispersion should include:

should use all the scores in the dist; should describe the average or typical deviation of the scores; increase in value as the scores become more diverse

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the sum of squared deviations will _______________ with sample size

increase

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using the median, range and IQR depicts both the _______________ and _____________________-

central tendency; variability

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horizontal line in the middle of the IQR box represents :

median

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scores that are beyond 3 times the height of the IQR box in either direction are termed:

extreme outliers (outliers are outside of 1.5 height of box or outside the whiskers)

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the standard deviation is ____________ for more diverse distributions and ______________ for less diverse distributions

higher; lower

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sigma of x-sub-I =

the sum of all data points

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t/f data that has a mean of 30 and a range of zero means there is littler variance

false - no variance

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if you take all data points in a sample and find the difference between the mean and the sum, the answer will always be?

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the sum of x sub i - x bar =

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limitations to mean:

outliers (extreme values) skew the mean

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Created by: aereal