# 5.5 Averages and probability

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By the end of this section, you will be able to:
• Calculate the mean of a set of numbers
• Find the median of a set of numbers
• Find the mode of a set of numbers
• Apply the basic definition of probability

Before you get started, take this readiness quiz.

1. Simplify: $\frac{4+9+2}{3}.$
If you missed this problem, review Multiply and Divide Mixed Numbers and Complex Fractions .
2. Simplify: $4\left(8\right)+6\left(3\right).$
If you missed this problem, review Use the Language of Algebra .
3. Convert $\frac{5}{2}$ to a decimal.
If you missed this problem, review Multiply and Divide Mixed Numbers and Complex Fractions .

One application of decimals that arises often is finding the average of a set of numbers. What do you think of when you hear the word average ? Is it your grade point average, the average rent for an apartment in your city, the batting average of a player on your favorite baseball team? The average is a typical value in a set of numerical data. Calculating an average sometimes involves working with decimal numbers. In this section, we will look at three different ways to calculate an average.

## Calculate the mean of a set of numbers

The mean    is often called the arithmetic average. It is computed by dividing the sum of the values by the number of values. Students want to know the mean of their test scores. Climatologists report that the mean temperature has, or has not, changed. City planners are interested in the mean household size.

Suppose Ethan’s first three test scores were $85,88,\text{and}\phantom{\rule{0.2em}{0ex}}94.$ To find the mean score, he would add them and divide by $3.$

$\begin{array}{}\\ \frac{85+88+94}{3}\\ \frac{267}{3}\\ 89\end{array}$

His mean test score is $89$ points.

## The mean

The mean    of a set of $n$ numbers is the arithmetic average of the numbers.

$\text{mean}=\frac{\text{sum of values in data set}}{n}$

## Calculate the mean of a set of numbers.

1. Write the formula for the mean
$\text{mean}=\frac{\text{sum of values in data set}}{n}$
2. Find the sum of all the values in the set. Write the sum in the numerator.
3. Count the number, $n,$ of values in the set. Write this number in the denominator.
4. Simplify the fraction.
5. Check to see that the mean is reasonable. It should be greater than the least number and less than the greatest number in the set.

Find the mean of the numbers $8,12,15,9,\text{and}\phantom{\rule{0.2em}{0ex}}6.$

## Solution

 Write the formula for the mean: $\text{mean}=\frac{\text{sum of all the numbers}}{n}$ Write the sum of the numbers in the numerator. $\text{mean}=\frac{8+12+15+9+6}{n}$ Count how many numbers are in the set. There are 5 numbers in the set, so $n=5$ . $\text{mean}=\frac{8+12+15+9+6}{5}$ Add the numbers in the numerator. $\text{mean}=\frac{50}{5}$ Then divide. $\text{mean}=10$ Check to see that the mean is 'typical': 10 is neither less than 6 nor greater than 15. The mean is 10.

Find the mean of the numbers: $8,9,7,12,10,5.$

8.5

Find the mean of the numbers: $9,13,11,7,5.$

9

The ages of the members of a family who got together for a birthday celebration were $16,26,53,56,65,70,93,\text{and}\phantom{\rule{0.2em}{0ex}}97$ years. Find the mean age.

## Solution

 Write the formula for the mean: $\text{mean}=\frac{\text{sum of all the numbers}}{n}$ Write the sum of the numbers in the numerator. $\text{mean}=\frac{16+26+53+56+65+70+93+97}{n}$ Count how many numbers are in the set. Call this $n$ and write it in the denominator. $\text{mean}=\frac{16+26+53+56+65+70+93+97}{8}$ Simplify the fraction. $\text{mean}=\frac{476}{8}$ $\text{mean}=59.5$

Is $59.5$ ‘typical’? Yes, it is neither less than $16$ nor greater than $97.$ The mean age is $59.5$ years.

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
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Bharti
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absolutely yes
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it is a goid question and i want to know the answer as well
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for teaching engĺish at school how nano technology help us
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Do somebody tell me a best nano engineering book for beginners?
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NANO
what is fullerene does it is used to make bukky balls
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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
what is the Synthesis, properties,and applications of carbon nano chemistry
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Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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