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
