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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: 4 + 9 + 2 3 .
    If you missed this problem, review Multiply and Divide Mixed Numbers and Complex Fractions .
  2. Simplify: 4 ( 8 ) + 6 ( 3 ) .
    If you missed this problem, review Use the Language of Algebra .
  3. Convert 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 , and 94 . To find the mean score, he would add them and divide by 3 .

85 + 88 + 94 3 267 3 89

His mean test score is 89 points.

The mean

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

mean = sum of values in data set n

Calculate the mean of a set of numbers.

  1. Write the formula for the mean
    mean = 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 , and 6 .

Solution

Write the formula for the mean: mean = sum of all the numbers n
Write the sum of the numbers in the numerator. mean = 8 + 12 + 15 + 9 + 6 n
Count how many numbers are in the set. There are 5 numbers in the set, so n = 5 . mean = 8 + 12 + 15 + 9 + 6 5
Add the numbers in the numerator. mean = 50 5
Then divide. mean = 10
Check to see that the mean is 'typical': 10 is neither less than 6 nor greater than 15. The mean is 10.
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Find the mean of the numbers: 8 , 9 , 7 , 12 , 10 , 5 .

8.5

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

9

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The ages of the members of a family who got together for a birthday celebration were 16 , 26 , 53 , 56 , 65 , 70 , 93 , and 97 years. Find the mean age.

Solution

Write the formula for the mean: mean = sum of all the numbers n
Write the sum of the numbers in the numerator. mean = 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. mean = 16 + 26 + 53 + 56 + 65 + 70 + 93 + 97 8
Simplify the fraction. mean = 476 8
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.

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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
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Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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Application of nanotechnology in medicine
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RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
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Nasa has use it in the 60's, copper as water purification in the moon travel.
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
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what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
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if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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Bob Reply
write examples of Nano molecule?
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The nanotechnology is as new science, to scale nanometric
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nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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Is there any normative that regulates the use of silver nanoparticles?
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what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
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what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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