Standard deviation (simply explained)
Summary
TLDRThis video script explains the concept of standard deviation as a measure of data dispersion around the mean. It outlines the process of calculating standard deviation using two different formulas, depending on whether the data represents a sample or the entire population. The script also differentiates between standard deviation and variance, emphasizing the importance of using standard deviation for easier data interpretation. A tip is provided to calculate standard deviation using an online tool, Beta Tab, for convenience.
Takeaways
- ๐ Standard deviation is a measure of how much data scatters around the mean, indicating the variability within a dataset.
- ๐งฎ To calculate the mean, sum all individual values and divide by the number of individuals in the dataset.
- ๐ Deviations from the mean are calculated by subtracting the mean from each individual data point.
- ๐ข The standard deviation is found by taking the square root of the average of the squared deviations from the mean.
- ๐ There are two formulas for standard deviation: one for a population (dividing by n) and one for a sample (dividing by n-1).
- ๐ The use of n-1 in the sample formula provides an unbiased estimate of the population standard deviation.
- ๐ The difference between standard deviation and variance is that variance is the square of the standard deviation, without taking the square root.
- ๐ The variance is the squared average distance from the mean, and it is the square of the standard deviation.
- ๐ Using standard deviation is recommended over variance for data interpretation as it retains the original data's unit of measurement.
- ๐ An online tool like Beta Tab can be used to calculate standard deviation easily by inputting data into a table on the website.
Q & A
What is standard deviation?
-Standard deviation is a measure of how much data scatters around the mean. It quantifies the average amount by which individual data points differ from the mean value.
How do you calculate the mean?
-The mean is calculated by summing the heights (or any other data points) of all individuals and dividing it by the number of individuals.
What does the standard deviation tell us about the data?
-The standard deviation tells us how much, on average, data points deviate from the mean, indicating the dispersion or spread of the data.
What is the formula for calculating standard deviation?
-The formula for calculating standard deviation is the square root of the sum of the squared deviations of each data point from the mean, divided by the number of values (n) or n-1 (depending on whether it's a sample or the entire population).
Why are there two different formulas for standard deviation?
-There are two formulas because one is used when you have the entire population (dividing by n) and the other is used when you have a sample of the population (dividing by n-1) to estimate the population standard deviation.
What is the difference between standard deviation and variance?
-Variance is the squared average distance from the mean, while standard deviation is the square root of the variance. Essentially, variance is the squared standard deviation.
Why is standard deviation preferred over variance when describing data?
-Standard deviation is preferred because it is in the same unit as the original data, making it easier to interpret and understand, whereas variance is in squared units which can be harder to interpret.
What is the relationship between the standard deviation and the original data units?
-The standard deviation is always in the same unit as the original data, which helps in making the measure of dispersion directly comparable to the data.
How can one calculate standard deviation easily?
-Standard deviation can be calculated easily using online tools like Beta Tab on datadept.net, where you simply copy your data into a table and select the variable to calculate.
What is the significance of the quadratic mean in standard deviation calculation?
-The quadratic mean is significant because using the arithmetic mean would always result in zero deviation due to positive and negative deviations canceling each other out. The quadratic mean avoids this by squaring the deviations before averaging.
What tip does the video provide for calculating standard deviation?
-The video suggests using online tools like Beta Tab on datadept.net for an easy calculation of standard deviation by simply entering the data into the provided table.
Outlines
๐ Understanding Standard Deviation
This paragraph introduces the concept of standard deviation as a measure of data dispersion around the mean. It explains how to calculate the mean, which is the sum of all individual heights divided by the number of individuals. The standard deviation quantifies how much each data point deviates from this mean, using an example where the mean height is 155 centimeters. The formula for standard deviation is presented, emphasizing the use of the square root of the sum of squared deviations divided by the number of values (n). The distinction between the arithmetic mean and the quadratic mean is highlighted, with the latter being essential for standard deviation calculations to avoid a zero result. The paragraph concludes with a note on the two formulas for standard deviation, one for the entire population (dividing by n) and one for samples (dividing by n-1), explaining the choice of formula based on whether the data represents a population or a sample.
๐ Calculating Standard Deviation and Variance
The second paragraph delves into the difference between standard deviation and variance. It clarifies that while standard deviation measures the average distance of data points from the mean, variance measures the squared average distance. The relationship between the two is such that variance is the square of standard deviation, and vice versa. However, variance often results in a unit that does not align with the original data, making standard deviation, which retains the original unit, more interpretable and preferable for data description. The paragraph also provides a practical tip for calculating standard deviation using an online tool called Beta Tab, accessible via datadept.net, where users can input their data, select the variable, and easily obtain the standard deviation. The video ends with a farewell, inviting viewers to look forward to the next video.
Mindmap
Keywords
๐กStandard Deviation
๐กMean
๐กData Scatter
๐กVariance
๐กSample
๐กPopulation
๐กArithmetic Mean
๐กQuadratic Mean
๐กSigma (ฯ)
๐กBeta Tab
Highlights
Standard deviation measures how much data scatters around the mean.
Calculating the mean involves summing all data points and dividing by their count.
Standard deviation quantifies the average deviation from the mean.
The formula for standard deviation involves squaring the deviations and taking the square root.
The arithmetic mean cannot be used for standard deviation calculation as it would always result in zero.
There are two formulas for standard deviation: one for population and one for sample data.
The population standard deviation is calculated using the formula with division by n.
The sample standard deviation uses the formula with division by n minus one to estimate the population standard deviation.
Variance is the squared average distance from the mean, as opposed to the standard deviation.
Variance is the square of the standard deviation, and its unit does not correspond to the original data.
Standard deviation is preferred over variance for data interpretation due to its ease of understanding and same unit as the original data.
A tip is provided for calculating standard deviation using an online tool called Beta Tab.
Datadept.net is recommended for easily calculating standard deviation by inputting data into a table.
The video concludes with a reminder to use standard deviation for sample data interpretation.
The presenter invites viewers to watch more videos and says goodbye.
Transcripts
today is about standard deviation after
this video you will know what standard
deviation is how you can calculate it
and why there are two different formulas
and finally what is the difference to
the variance
at the end of this video i have a tip
for you so let's get started
so what is the standard deviation the
standard deviation is a measure of how
much your data scatters around the mean
so the standard deviation has something
to do with the scatter of your data for
example how different the answers of
your respondents are
here's an example
let's say you measure the height of a
small group of people
the standard deviation tells us how much
your data scatters around the mean
so we first need to calculate the mean
you can get a mean simply by summing the
heights of all individuals and dividing
it by the number of individuals
let's say we get a mean value of
155 centimeters
now we want to know how much each person
deviates from the mean
so we look at the first person who
deviates 18 centimeters from the mean
value the second person deviates 8
centimeters from the mean value
and so on
finally person number six deviates six
centimeters from the mean value
so simply said people that are very
small or very tall deviate more from the
mean value
now of course you're not interested in
the deviation of each individual person
from the mean value
but you want to know how much the
persons deviate from the mean value on
average
so how much do these persons on average
deviate from the mean value this is what
the standard deviation tells us
in our example the average deviation
from the mean value is
12.06 centimeters and now of course the
next question is how can we calculate
the standard deviation you can calculate
the standard deviation with the
following formula
sigma is the standard deviation
n is the number of persons
x i is the size of one single person and
x dash is the mean value of all people
so the standard deviation is the root of
the sum of square deviations divided by
the number of values
for our example this means that we
calculate the size of the first person
minus the mean and square that then the
size of the second person minus the mean
and then square that and so on until we
arrive at the last person
then we divide this number by the number
of people so 6 and take the root of it
the result is then
12.06 centimeters
so each individual person has some
deviation from the mean
but on average the people deviate 12.06
centimeters from the mean
which is now our standard deviation
now you might notice one thing i always
talk about the average deviation from
the mean
but for the average deviation i would
actually just add up all deviations and
divide it by the number of participants
just like you calculate a mean value
right
you're absolutely right but there are
different mean values
in the case of the standard deviation
it's not the arithmetic mean which is
used
but the quadratic mean
if the arithmetic mean would be used the
result would be zero every time
so far so good but now there's one more
thing to consider
there are two slightly different
formulas for the standard deviation in
the first formula there is a deviation
by n and in the other one there is a
deviation by n minus one
but why that why are there two different
formulas
usually you want to know the standard
deviation of the whole population for
example you want to know the standard
deviation of hate of all american
professional soccer players
now if you had the hate of all american
soccer players
you would take this equation with one
divided by n
however it is usually not possible to
investigate the entire population
so you take a sample
then you use this sample to estimate the
standard deviation of the population
in that case you use this formula
therefore whenever you have data of the
whole population and you want to
calculate the standard deviation for
just this data you use 1 divided by n
therefore
whenever you have data of the whole
population and you want to calculate the
standard deviation for just this data
you use 1 divided by n
if you only have one sample and you want
to estimate the standard deviation you
use n minus 1.
so to keep it simple if your survey
doesn't cover the whole population you
always use the formula on the right side
likewise if you have conducted a
clinical study for example
then you also use the formula on the
right side to infer the population
let's look at the next question now
what is the difference between the
standard deviation and the variance
as you now know the standard deviation
is the average distance from the mean
the variance now is the squared average
distance from the mean
so we have one and the same formula the
only difference is that in order to
calculate the standard deviation we take
the root
in order to calculate the variance we
don't do that to put it the other way
around the variance is the squared
standard deviation and the standard
deviation is the root of the variance
however this squaring results in a
figure which is quite difficult to
interpret
since the unit of the calculated
variance does not correspond to the
original data
for this reason it is advisable to
always use the standard deviation to
describe a sample as this makes
interpretation a lot easier for you
the standard deviation is always in the
same unit as the original data
in our example this would be centimeters
and finally as promised i have a tip for
you
if you want to calculate the standard
deviation you can easily do it online
with beta tab
just visit datadept.net
copy your data into the table
select the variable you want to
calculate
and afterwards you will get the standard
deviation in a very easy way
i hope you enjoyed the video and see you
next time bye bye
you
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