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A summary of useful formulas used in examining descriptive statistics

    Commonly used symbols

  • The symbol Σ means to add or to find the sum.
  • n = the number of data values in a sample
  • N = the number of people, things, etc. in the population
  • x ¯ size 12{ {overline {x}} } {} = the sample mean
  • s = the sample standard deviation
  • μ = the population mean
  • σ = the population standard deviation
  • f = frequency
  • x = numerical value

    Commonly used expressions

  • x * f = A value multiplied by its respective frequency
  • x size 12{ Sum {x} } {} = The sum of the values
  • x * f size 12{ Sum {x} times f} {} = The sum of values multiplied by their respective frequencies
  • ( x x ¯ ) or ( x μ ) = Deviations from the mean (how far a value is from the mean)
  • ( x x ¯ ) 2 or ( x μ ) 2 = Deviations squared
  • f ( x x ¯ ) 2 or f ( x μ ) 2 = The deviations squared and multiplied by their frequencies

Mean Formulas:

  • x ¯ = size 12{ {overline {x}} ={}} {} x n size 12{ { { Sum {x} } over {n} } } {} or x ¯ = size 12{ {overline {x}} ={}} {} f · x n size 12{ { { Sum {f times x} } over {n} } } {}
  • μ = size 12{μ={}} {} x N size 12{ { { Sum {x} } over {N} } } {} or μ size 12{μ} {} = f · x N size 12{ { { Sum {f times x} } over {N} } } {}

Standard Deviation Formulas:

  • s = size 12{s={}} {} Σ ( x x ¯ ) 2 n 1 or s = size 12{s={}} {} Σ f · ( x x ¯ ) 2 n 1
  • σ = size 12{σ={}} {} Σ ( x μ ¯ ) 2 N or σ = size 12{σ={}} {} Σ f · ( x μ ¯ ) 2 N

Formulas Relating a Value, the Mean, and the Standard Deviation:

  • value = mean + (#ofSTDEVs)(standard deviation), where #ofSTDEVs = the number of standard deviations
  • x size 12{x} {} = x + (#ofSTDEVs)( s )
  • x size 12{x} {} = μ size 12{μ} {} + (#ofSTDEVs)( σ )

Questions & Answers

what is the stm
Brian Reply
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
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Source:  OpenStax, Collaborative statistics (custom online version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11476/1.5
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