2300 - Chapter 3

mean as a balance point

below the mean has the same points/distance as above the mean

difference of "bimodal" and "multimodal"

bimodal only has 2 modes in a score, but multimodal has more than 2 major mode: tallest peak minor mode: shorter peak

what's used to represent the best value for all the individuals?

central tendency

what's the goal of "central tendency"

find the best representative value for all the individuals in a distribution

skewed distribution

for continuous variable, strong tendency for mean, median, mode to be predictable

when two modes have unequal frequencies

major mode: taller peak minor mode: shorter peak

central tendency for a ratio scale

mean median mode

what's usually the best measure for central tendency? why use the others?

mean is usually best mode and median is used when it's impossible to compute the mean or the mean isn't an accurate representation

what are the three methods for determining the central tendency?

mean, median, mode

central tendency for a ordinal scale

median mode

the mean isn't always in the ______ of the group

middle

central tendency for a nominal scale

mode

facts about the mode

no symbol generally the only measure for nominal scale only measure of tendency that corresponds to an actual score

mean

score of the scores divided by number of scores ("average") useful for finding the total using the M and n

mode

score/category that has the highest frequency mode has no symbol

minor mode

shorter peak when two modes are not equal in a bimodal distribution

multimodal

a distribution that has more than 2 modes

introducing a new score or removing

adding or removing a score that's identical to the mean won't change the mean

adding/subtracting a constant from each score

adding/removing a value to every score adds/removes the same constant to the mean

changing a score of a mean

change in a single score changes sigma-X and the M

bimodal

distribution that has 2 modes

2 shapes of distribution

symmetrical and skewed

what measure can't be applied to an ordinal scale

the mean: average of all scores

median

the midpoint of the distribution (has no symbol)

four other characteristics of the mean

1. changing a score 2. introducing a new score or removing 3. adding/subtracting a constant from each score 4. multiplying/dividing each score by a constant

four situations that make the "median" useful

1. extreme scores/skewed distribution - extreme value inflates/distorts the M 2. undetermined values - when there's no score for an individual 3. open-ended distributions - when a distribution has no upper/lower limit ("5 or more") 4. ordinal scale - since you can't determine distance, only the order/direction

3 situations for using the mode

1. nominal scale- since there's no way in finding distance/direction 2. discrete variable- since they're whole, indivisible categories, you can't have "4.7" 3. describing shape- mode requires no calculation, so mode is used to supplement the mean

symmetrical distribution

if perfect or roughly symmetrical, the mean will be close together, mode will be too unless it's bimodal

multiplying/dividing each score by a constant

if score is multiplied or divided, same way to the mean ie. changing units of measurement

positively skewed distribution

starts high then tapers off: mode -> median -> mean

negatively skewed distribution

starts low then climbs high: mean -> median -> mode

central tendency

statistical measure to determine a single score that defines the center of a distribution

major mode

taller peak when two modes are not equal in a bimodal distribution

difference of mean and median

they both define and measure central tendency, but the meaning of "middle" is different

the 2 symbols for mean

u = population M = sample

what's the symbol for the "mean" symbol for mode and median?

u or M no symbol for mode and median