10022013 Variability & Central tendency (3b&4)
October 2, 2013
6:01 PM
Last Week Distributions…
Inferential statistics - using scores from the samples to make generalizations for the whole
population;
Population - refers to entire group of individuals that interested
Parameter - statistics of a population
Sample - selected group to use for study ; used to make inferences for population
Statistic - scores from the samples
Central tendency - a single value/score that’s the best to describe all; center of the distribution; 3
different methods used in specific situations
Mean - average= ƩX/(N or n); population mean notified as µ ( =ƩX/N); sample mean - can be used
as estimate of pop. Mean, notified as M = ΣX / n; equal distribution within sample/ population; if
given mean and score multiple the 2 to get the ƩX; can be a balance point - distnace above and
below value (total of values from before and after mean number) is the same; if muliplying or
dividing by a constant mean will be affected in the same way; possible to have more than 50% of
score above the mean number
o Weighted mean - finding the mean with more than one sample one sample ; combine all
scores and find mean using all participants
A mean should not be used with extreme scores, skewed distributions, ordinal or nominal
scales, undetermined variables (didn’t finish scoring - cannot be used/only on ordinal scale),
and open ended distributions (aged 25 + - ); in these situations median is more appropriate
Median - the middle number - unrelated to distance between variable and median point, it is the
midpoint of all variables if no middle number use 2 mid numbers and average them; can be the
same as mean but doesn't have to be; dividing score into 2 equal groups, scores are 50/50 (above
and below median variable);
o
Precise median - located in interval between real limits; used with continuous variables;
number of scores (fraction) of scores that fall within the real limits; remember there must
be equal distribution on either side of the median variable, so to find precise median figure
out how many more intervals are needed below median and divide by how many times an
interval falls on the median variable
***same as finding the 50th percentile
Stem and leaf plots- make sure in numerical order
Mode - most frequent score / observation; can be used for any types of data, but may be less
helpful; corresponds to actual scores in the data set,
o Bimodal/multimodal - possible to have more than one mode if there are more than one
variable with the same frequency; if frequencies are all very similar (with many high points)
there is no mode
o Main and minor mode - which indicates there is a another variable with similar frequency to
the mode;
o Mode should be used for discrete variables, nominal scales, describing shape, or as a
supplementary measure
Graphing Means usually presented using graphs, used to compare between different groups or conditions,
type of graph depends on scale of measurement that was used with the independent variable
(nominal/interval) ex. Nominal scale could use a bar graph or histogram; interval scale would need
a scatter plot
Likert scales - meant to be equidistant/symmet

More
Less