馃攳
Standard deviation (simply explained) - YouTube
Channel: unknown
[0]
today is about standard deviation after
[3]
this video you will know what standard
[5]
deviation is how you can calculate it
[8]
and why there are two different formulas
[11]
and finally what is the difference to
[13]
the variance
[15]
at the end of this video i have a tip
[17]
for you so let's get started
[19]
so what is the standard deviation the
[22]
standard deviation is a measure of how
[24]
much your data scatters around the mean
[28]
so the standard deviation has something
[30]
to do with the scatter of your data for
[33]
example how different the answers of
[36]
your respondents are
[38]
here's an example
[40]
let's say you measure the height of a
[42]
small group of people
[45]
the standard deviation tells us how much
[48]
your data scatters around the mean
[51]
so we first need to calculate the mean
[54]
you can get a mean simply by summing the
[57]
heights of all individuals and dividing
[60]
it by the number of individuals
[64]
let's say we get a mean value of
[66]
155 centimeters
[69]
now we want to know how much each person
[72]
deviates from the mean
[75]
so we look at the first person who
[77]
deviates 18 centimeters from the mean
[80]
value the second person deviates 8
[83]
centimeters from the mean value
[86]
and so on
[87]
finally person number six deviates six
[91]
centimeters from the mean value
[94]
so simply said people that are very
[96]
small or very tall deviate more from the
[100]
mean value
[102]
now of course you're not interested in
[104]
the deviation of each individual person
[107]
from the mean value
[109]
but you want to know how much the
[111]
persons deviate from the mean value on
[113]
average
[115]
so how much do these persons on average
[118]
deviate from the mean value this is what
[121]
the standard deviation tells us
[124]
in our example the average deviation
[127]
from the mean value is
[129]
12.06 centimeters and now of course the
[132]
next question is how can we calculate
[135]
the standard deviation you can calculate
[138]
the standard deviation with the
[140]
following formula
[142]
sigma is the standard deviation
[145]
n is the number of persons
[148]
x i is the size of one single person and
[151]
x dash is the mean value of all people
[156]
so the standard deviation is the root of
[159]
the sum of square deviations divided by
[163]
the number of values
[165]
for our example this means that we
[167]
calculate the size of the first person
[170]
minus the mean and square that then the
[173]
size of the second person minus the mean
[176]
and then square that and so on until we
[179]
arrive at the last person
[182]
then we divide this number by the number
[184]
of people so 6 and take the root of it
[189]
the result is then
[191]
12.06 centimeters
[194]
so each individual person has some
[196]
deviation from the mean
[198]
but on average the people deviate 12.06
[203]
centimeters from the mean
[205]
which is now our standard deviation
[208]
now you might notice one thing i always
[211]
talk about the average deviation from
[214]
the mean
[215]
but for the average deviation i would
[218]
actually just add up all deviations and
[221]
divide it by the number of participants
[224]
just like you calculate a mean value
[227]
right
[228]
you're absolutely right but there are
[230]
different mean values
[232]
in the case of the standard deviation
[235]
it's not the arithmetic mean which is
[237]
used
[238]
but the quadratic mean
[240]
if the arithmetic mean would be used the
[243]
result would be zero every time
[247]
so far so good but now there's one more
[249]
thing to consider
[251]
there are two slightly different
[253]
formulas for the standard deviation in
[255]
the first formula there is a deviation
[258]
by n and in the other one there is a
[261]
deviation by n minus one
[264]
but why that why are there two different
[266]
formulas
[268]
usually you want to know the standard
[269]
deviation of the whole population for
[272]
example you want to know the standard
[274]
deviation of hate of all american
[277]
professional soccer players
[280]
now if you had the hate of all american
[283]
soccer players
[284]
you would take this equation with one
[287]
divided by n
[290]
however it is usually not possible to
[292]
investigate the entire population
[295]
so you take a sample
[298]
then you use this sample to estimate the
[301]
standard deviation of the population
[304]
in that case you use this formula
[307]
therefore whenever you have data of the
[309]
whole population and you want to
[312]
calculate the standard deviation for
[314]
just this data you use 1 divided by n
[318]
therefore
[319]
whenever you have data of the whole
[322]
population and you want to calculate the
[324]
standard deviation for just this data
[328]
you use 1 divided by n
[331]
if you only have one sample and you want
[334]
to estimate the standard deviation you
[337]
use n minus 1.
[339]
so to keep it simple if your survey
[342]
doesn't cover the whole population you
[345]
always use the formula on the right side
[348]
likewise if you have conducted a
[350]
clinical study for example
[353]
then you also use the formula on the
[355]
right side to infer the population
[359]
let's look at the next question now
[361]
what is the difference between the
[363]
standard deviation and the variance
[366]
as you now know the standard deviation
[369]
is the average distance from the mean
[372]
the variance now is the squared average
[376]
distance from the mean
[378]
so we have one and the same formula the
[381]
only difference is that in order to
[384]
calculate the standard deviation we take
[386]
the root
[387]
in order to calculate the variance we
[390]
don't do that to put it the other way
[392]
around the variance is the squared
[395]
standard deviation and the standard
[397]
deviation is the root of the variance
[401]
however this squaring results in a
[404]
figure which is quite difficult to
[406]
interpret
[408]
since the unit of the calculated
[410]
variance does not correspond to the
[413]
original data
[414]
for this reason it is advisable to
[417]
always use the standard deviation to
[419]
describe a sample as this makes
[422]
interpretation a lot easier for you
[425]
the standard deviation is always in the
[427]
same unit as the original data
[430]
in our example this would be centimeters
[433]
and finally as promised i have a tip for
[435]
you
[436]
if you want to calculate the standard
[438]
deviation you can easily do it online
[441]
with beta tab
[443]
just visit datadept.net
[446]
copy your data into the table
[448]
select the variable you want to
[450]
calculate
[452]
and afterwards you will get the standard
[454]
deviation in a very easy way
[458]
i hope you enjoyed the video and see you
[460]
next time bye bye
[468]
you
Most Recent Videos:
You can go back to the homepage right here: Homepage