Measures of central tendency
Measures of central tendency are those that describe the middle of a sample.
Mean
The mean or average of a set of data (more accurately, the arithmetic mean) is calculated by adding up all of the individual values within the data set and dividing the result by the number of values.
Mean formula
xi to xn are the values of all of the data points in the set
n is the number of data points in the set
Mean values are a good indicator of central tendency when ...
... all of the values tend to be fairly close to one another.
Outlier
An extremely large or extremely small value compared to the other data values
Median
The median value for a set of data is its midpoint, where half of data points are greater than the value and half are smaller. In data sets with an odd number of values, the median will actually be one of the data points. In data sets with an even number of values, the median will be the mean of the two central data points.
Median position
n is the number of data values
The median tends to be the _____ of the common measures of central tendency.
least susceptible to outliers
The median may not be useful for data sets with _____ or _____.
very large ranges
multiple modes
If the mean and the median are far from each other, this implies ...
... the presence of outliers or a skewed distribution.
Mode
The mode, quite simply, is the number that appears the most often in a set of data. There may be multiple modes in a data set, or—if all numbers appear equally—there can even be no mode for a data set.
When we examine distributions, the _____ represent modes.
peaks
The mode is _____ as a measure of central tendency.
not typically used