General Calculation of Standard Deviation Video Lecture | Mathematics for GRE Paper II

how to calculate standard deviation how
many vegetables do you have in your
fridge is that a common amount or are
you an outlier we can use standard
deviation to know whether someone's
behavior is normal or extraordinary
standard deviation often calculated
along with the mean of a data set tells
us how spread out the data is it is used
for data that is normally distributed
and can be easily calculated using a
graphing calculator or spreadsheet
software but it can also be calculated
with a few math operations we're going
to use an example involving the number
of vegetables five of our friends have
in their fridges they have two three
four seven and nine vegetables we
calculate the standard deviation the
first step is to calculate the mean of
the data set denoted by X with a line
over it also called x-bar in this case
the mean would be 2 plus 3 plus 4 plus 7
plus 9 divided by 5 which equals 5
our average friend has five vegetables
in their fridge the second step is to
subtract the mean from each data point
to find the differences it's helpful to
use a table like this 2 minus 5 equals
negative 3 3 minus 5 equals negative 2 4
minus 5 equals negative 1 7 minus 5
equals 2 and 9 minus 5 equals 4 the
third step is to square each difference
this makes all the difference is
positive so they don't cancel each other
out and it also magnifies larger
differences and minimizes smaller
differences negative 3 squared equals 9
negative 2 squared equals 4 negative 1
squared equals 1 2 squared equals 4 and
4 squared equals 16 the fourth step is
to calculate the mean of the squared
differences 9 plus 4 plus 1 plus 4 plus
16 divided by 5 equals 6 point 8
the final step is to take the square
root this counteracts the squaring we
did earlier and allows the standard
deviation to be expressed in the
original units the square root of 6.8 is
about 2.6 and that's the standard
deviation we're done the mean number of
vegetables is five with a standard
deviation of two point six veggies
knowing that about two-thirds of the
data fall within one standard deviation
of the mean assuming the data is
normally distributed we can say that
about two-thirds of our friends have
between two point four and seven point
six vegetables in their fridges to recap
these are the five steps for calculating
standard deviation calculate the mean
subtract the mean from each data point
square each difference calculate the
mean of the squared differences and take
the square root using symbols the
equation for calculating standard
deviation looks like this lowercase
Sigma stands for standard deviation of a
population upper case Sigma tells us to
calculate the sum for each instance X is
each data point x-bar is the mean of the
data points and n is the number of data
points keep in mind that there is a
similar formula that divides by n minus
1 that formula is used when you only
have data for a sample of the population
hope this was helpful see you next time
you