What is Standard Deviation? Video Lecture | Mathematics for GRE Paper II

have we discovered a new particle in
physics is a manufacturing process out
of control what percentage of men are
taller than LeBron James
how about taller than Yao Ming all these
questions can be answered using the
concept of standard deviation for any
set of data the mean and standard
deviation can be calculated for example
five people may have the following
amounts of money in their wallets twenty
one fifty sixty to eighty five and
ninety dollars the mean is sixty one
dollars and sixty cents and the standard
deviation is twenty eight dollars and
one cent how much does the data vary
from the average standard deviation is a
measure of spread that is how spread out
a set of data is a low standard
deviation tells us that the data is
closely clustered around the mean or
average while a high standard deviation
indicates the data is dispersed over a
wider range of values standard deviation
is used when the distribution of data is
approximately normal resembling a bell
curve standard deviation is commonly
used to understand whether a specific
data point is standard and expected or
unusual and unexpected standard
deviation is represented by the
lowercase Greek letter Sigma a data
points distance from the mean can be
measured by the number of standard
deviations that it is above or below the
mean a data point that is beyond a
certain number of standard deviations
from the mean represents an outcome that
is significantly above or below the
average this can be used to determine
whether a result is statistically
significant or part of expected
variation such as whether a bottle with
an extra ounce of soda is to be expected
or warrants further investigation into
the production line the 6895 99.7 rule
tells us that about 68% of the data fall
within one standard deviation of the
mean about 95 percent of data fall
within to thinner deviations of the mean
and about ninety-nine point seven
percent of data fall within three
standard deviations of the mean the
average height of an American adult male
is 510
with a standard deviation of three
inches using the 6895 99.7 rule this
means that 68% of American men are 510
plus or minus three inches 95 percent of
American men are 510 plus or minus six
inches and ninety-nine point seven
percent of American men are 510 plus or
minus nine inches so this means only
about 0.3 percent of American men
deviate more than nine inches from the
average with 0.15 percent taller than
six seven and point one five percent
shorter than five one this reasoning
suggests that LeBron James is one in two
thousand five hundred and Yao Ming is
one in 450 million in particle physics
scientists have what are called five
Sigma results results that are five
standard deviations above or below the
mean a result that varies this much can
signify a discovery as it has only a 1
in 3.5 million chance that it is due to
random fluctuation in summary standard
deviation is a measure of spread along
with the mean the standard deviation
allows us to determine whether AZ value
is statistically significant or part of
expected variation
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