Chapter Four: Numerical Descriptors of Data
•
Numerical measures calculated from data are either
statistics
or
data.
o
Statistic –
numerical descriptor that is calculated from sample data and is used to describe the sample. Statistics
are usually represented by Roman letters.
o
Parameter –
numerical descriptor that is used to describe a population. Parameters are usually represented by
Greek letters.
•
Measures of Central Tendency
o
Sample Mean –
center of balance of a set of data and is found by adding up all of the data values and dividing
by the number of observations.
=
sum of all values in the sample
Total # of observations
o
Population Mean –
represented by Greek letter mu
o
Sample Median –
value of the middle of observation in an ordered set of data.
Step One –
If the number of observations in the sample
n
is odd, then the median is the value of the
observation in the (n+1)/2 position
Step Two –
If
n
is even, then the median is the average of the values in the n/2 and n/2+1 positions.
o
Sample Mode –
data value that has the highest frequency of occurrence in the sample
Depending on size of sample and number of possible data values, there may not be any repeated
values in the sample
May appear to be more than one mode for a sample
•
Frequent in small samples
•
Most values happen to occur more than once.
•
Bimodal – two modes
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 Fall '07
 DiAGNE
 Standard Deviation

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