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Measures of Central Tendency
The mean is the average of all numbers and is sometimes called
the arithmetic mean. To calculate mean, add together all of the numbers in
a set and then divide the sum by the total count of numbers.
The statistical median is the middle number in a sequence of numbers. To
find the median, organize each number in order by size; the number in the
middle is the median.
The mode is the number that occurs most often within a set of numbers.
Measures of Variability
The range is the difference between the highest and lowest values within a
set of numbers. To calculate range, subtract the smallest number from the
largest number in the set.
The interquartile range is a measure of where the “middle fifty” is in a data
set. Where a range is a measure of where the beginning and end are in a
set, an interquartile range is a measure of where the bulk of the values
lie. That’s why it’s preferred over many other measures of spread (i.e.
the average or median) when reporting things like school performance or
test scores. The interquartile range formula is the first quartile subtracted
from the third quartile.
Standard Deviation
The standard deviation is a statistic that tells you how tightly all the various
examples are clustered around the mean in a set of data. Its symbol
is σ (the lower case greek letter sigma).
When the examples are pretty tightly bunched together and the bell-shaped
curve is steep, the standard deviation is small. When the examples are
spread apart and the bell curve is relatively flat, that tells you have a
relatively large standard deviation. Standard deviation is a measure of
the dispersion of a set of data from its mean. If the data points are further
from the mean, there is higher deviation within the data set. Standard
deviation is calculated as the square root of variance by determining the
variation between each data point relative to the mean.