# 2.11 Summary of formulas

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A summary of useful formulas used in examining descriptive statistics

## Commonly used symbols

• The symbol $\Sigma$ 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
• $\overline{x}$ = the sample mean
• $s$ = the sample standard deviation
• $\mu$ = the population mean
• $\sigma$ = the population standard deviation
• $f$ = frequency
• $x$ = numerical value

## Commonly used expressions

• $x*f$ = A value multiplied by its respective frequency
• $\sum x$ = The sum of the values
• $\sum x*f$ = The sum of values multiplied by their respective frequencies
• $\left(x-\overline{x}\right)$ or $\left(x-\mu \right)$ = Deviations from the mean (how far a value is from the mean)
• ${\left(x-\overline{x}\right)}^{2}$ or ${\left(x-\mu \right)}^{2}$ = Deviations squared
• ${f\left(x-\overline{x}\right)}^{2}$ or ${f\left(x-\mu \right)}^{2}$ = The deviations squared and multiplied by their frequencies

Mean Formulas:

• $\overline{x}=$ $\frac{\sum x}{n}$ or $\overline{x}=$ $\frac{\sum f·x}{n}$
• $\mu =$ $\frac{\sum x}{N}$ or $\mu$ = $\frac{\sum f·x}{N}$

Standard Deviation Formulas:

• $s=$ $\sqrt{\frac{\Sigma {\left(x-\overline{x}\right)}^{2}}{n-1}}$ or $s=$ $\sqrt{\frac{\Sigma {f·\left(x-\overline{x}\right)}^{2}}{n-1}}$
• $\sigma =$ $\sqrt{\frac{\Sigma {\left(x-\overline{\mu }\right)}^{2}}{N}}$ or $\sigma =$ $\sqrt{\frac{\Sigma {f·\left(x-\overline{\mu }\right)}^{2}}{N}}$

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

• value = mean + (#ofSTDEVs)(standard deviation), where #ofSTDEVs = the number of standard deviations
• $x$ = $\overline{x}$ + (#ofSTDEVs)( $s$ )
• $x$ = $\mu$ + (#ofSTDEVs)( $\sigma$ )

what is the stm
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what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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