the goal of central tendency is to
find the single score that is most typical or most representative of the entire group
the mean is calculated by:
the sum of the scores divided by the number of the scores
if you see "M" when referring to mean, we are talking about a _____.
do we use n or N when making the equation?
sample.
divide by "n".
if you see "u" when referring to mean, we are talking about a ______.
do we use n or N?
population mean.
divide by "N
central tendency: the greatest frequency is the
mode
the average of all scores is the
mean
the midpoint is the
median
what is the preferred measures of central tendency?
mean
can there be two or even 3 measures of central tendency for the same set of data?
yes
when would it be more appropriate to use a median?
1. extreme scores or skewed distributions
2. undetermined values
3. open-ended distribution
4. ordinal scale
why would it be more appropriate to use a median in cases of extreme scores or skewed distributions?
the median is not easily affected by extreme scores, however extreme scores inflate the value of the ?X and distort the mean
why would it be more appropriate to use a median in cases of undetermined values? give an example
it is not possible to compute an undetermined value, so ?X cannot be calculated.
E.g. a person never completes the puzzle, after an hour the experimenter stops the experiment. This gives an undetermined value.
why would it be more appropriate to use a median in cases of open -ended distributions? give an example.
there is no upper limit (or lower limit) for one of the categories, so it is impossible to compute the mean.
E.g. a category is "5 or more pizza's" - this is an open ended category.
why would it be more appropriate to use a median in cases of an ordinal scale?
because the mean is defined in terms of distances, and ordinal scales do not measure distance therefor it is not appropriate to compute a mean for scores from an ordinal data.
What are the 3 situations where a mode is commonly used as an alternative to the mean, or used in conjunction with the mean to describe central tendency?
1. nominal scales
2. discrete variables
3. describing shape
explain why it would be appropriate to use a mode in the case of nominal scales.
because categories on nominal scales are differentiated only by name. no quantity (distance/direction) is measured.
what is the primary advantage of the mode/ when is it used mostly?
the fact that it can be used to measure and describe central tendency for data measured on a nominal scale.
the mode is the ONLY option for describing central tendency for nominal data.
explain why it would be appropriate to use a mode in the case of discrete variables: Give an example.
discrete variables are numerical values, so it is possible to calculate means. However, in calculating a mean you will usually get a fractional value that cannot exist.
E.g. if amount of children is calculated and the mean age is 2.4, this is physically i
explain why it would be appropriate to use a mode in the case of describing shape.
the mode requires little or no calculation.
it is included as a supplementary measure along with mean or median as an extra piece of information. the mode identifies the peak(s) in frequency, so you can get a better picture of the distribution using the m
how would you abbreviate mean and median and mode?
mean = M
median = Mdn
mode = no abbreviation
the means or medians are displayed using (3 things)
line graph, histogram, or a bar graph.
when are the mean and median the same?
when will the mode be the same as well?
...when are the mode/mean/median similar, but not the same?
in a symmetrical distribution they are the same.
if the symmetrical distribution only has one mode, then this will be the same as well.
in a roughly symmetrical distribution the three measures are clustered together.
when are the mode, median and mean located in predictably different situations?
in skewed distributions especially distribution of continuous variables.
where would the mean/median/mode be located (from left to right) on a negatively skewed distribution?
1. mean
2. median
3. mode
where would the mean/median/mode be located (from left to right) on a positively skewed distribution?
1. mode
2. median
3. mean