Welcome to IRSC

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Welcome to IRSCs LIVE Virtual Lesson on

• Mean, Median, Mode, and Range
• Instructor Mrs. DiMartino

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How to participate in this session
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What you will learn today

• How to define and compute
• a) the mean
• b) the median
• c) the mode
• d) the range of a set of data.

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Why learn these skills?

• We use statistics such as the mean, median, mode,
  and range to obtain information about a
  population (group) from our sample set of
  observed values (data).

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Mean

• The mean is the average of a set of numbers.
•  

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How to find the mean?

• Add up all the numbers.
• 2. Then, divide by how many numbers there are.
• In other words, it is the sum divided by the
  count.

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Example 1 Finding the Mean

• What is the mean of these numbers?
• 6, 11, 7
• Add the numbers
• 6 11 7 24
• Divide by how many numbers there are (3)
• 24 / 3 8
• The Mean is 8

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Example 2 Finding the Mean

• What is the mean of these numbers?
• 94, 88, 100, 65, 89, 70
• Add the numbers
• 94 88 100 65 89
  70 506
• 2. Divide by how many numbers there are (6)
• 506 / 6 84.3
• The mean is 84.3

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Example 3 Finding the Mean

• What is the mean of these numbers?
• 24.00, 16.00, 18.00, 34.00
• 1. Add the numbers.
• 24.00 16.00 18.00 34.00 92.00
• 2. Divide the total by how many there are.
• 92.00/4 23.00
• The mean is 23

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Median

• The median is the
• "middle number"
• in a list of numbers that have been sorted by
  value.

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How to find the median?

• 1. Place the numbers you are given in value
  order.
• 2. Find the middle number.

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Example 1 Finding the Median

• Find the median of
• 6, 3, 7, 9, 4
• Place the numbers you are given in value order.
  3, 4, 6, 7, 9
• Find the middle number.
• 3, 4, 6, 7, 9
  
• The median is 6

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Example 2 Finding the median

• Find the median of
• 12, 2, 6, 9, 7, 8
• Place the numbers you are given in value order.
  2, 6, 7, 8, 9, 12
• Find the middle number.
• 2, 6, 7, 8, 9,
  12
• Wait a minute! There isnt a middle
  number!!!

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Median (Ex2 continued)

• When there are two numbers in the middle
• Locate the two middle numbers. (7 and 8)
• Add them together. 8 7 15
• Divide that number by 2. 15 / 2 7 ½
• The median is 7 ½

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Example 3 Finding the Median

• Find the median of
• 4, 9, 5, 13, 7
• Place the numbers you are given in value order.
  4, 5, 7, 9, 13
• Find the middle number.
• 4, 5, 7, 9, 13
• The median is 7

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Mode

• The mode is simply
• the number that
• appears
• most often.

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How to Find the Mode?

• First, put the numbers in order.
• Then count how many there are of each number.
• Find the most frequently occurring number.

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Example 1 Finding the Mode

• Find the mode of these numbers
• 3, 6, 7, 8, 7, 3, 2, 7, 9
• First, put the numbers in order.
• 2, 3, 3, 6, 7, 7, 7,
  8, 9
• Then count how many there are of each number.
  Which number occurred most frequently? 2, 3,
  3, 6, 7, 7, 7, 8, 9
• The mode is 7

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Example 2 Finding the Mode(when there is more
than 1 mode)

• Find the mode of these numbers
• 3, 3, 2, 3, 6, 4, 8, 6, 6, 4
• First, put the numbers in order.
• 2, 3, 3, 3, 4, 4, 6, 6,
  6, 8
• Then count how many there are of each number.
  Which number occurred most frequently?
  2, 3, 3,
  3, 4, 4, 6, 6, 6, 8
• The modes are 3 and 6

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Example 3 Finding the Mode

• Find the mode of these numbers
• 12, 9, 11, 6, 4, 3, 12, 8, 9, 12
• First, put the numbers in order.
• 3, 4, 6, 8, 9, 9, 11,
  12, 12, 12
• Then count how many there are of each number.
  Which number occurred most frequently?
• 3, 4, 6, 8, 9, 9, 11,
  12, 12, 12
• The mode is 12

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Range

• The "range" is the
• difference between
• the largest and smallest values (numbers)
• of a set.

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How to find the range?

• First, put the numbers in order.
• Locate the largest number and the smallest
  number.
• Then subtract them to find the range.

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Example 1 Finding the Range

• Find the range of this set of numbers
• 4, 2, 6, 9, 7, 15, 3, 5, 6
• First, put the numbers in order.
• 2, 3, 4, 5, 6, 6, 9,
  7, 15
• 2. Locate the largest number and the smallest
  number. 15 and 2
• 3. Then subtract them to find the range. 15-2
  13

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Example 2 Finding the range

• Find the range of this set of numbers
• 22, 16, 17, 8, 12
• First, put the numbers in order.
• 8, 12, 16, 17,
  22
• 2. Locate the largest number and the smallest
  number. 22 and 8
• 3. Then subtract them to find the range. 22-8
  14

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Example 3 Finding the Range

• Find the range of this set of numbers
• 1, 3, 9, 4, 20, 6
• First, put the numbers in order.
• 1, 3, 4, 6, 9,
  20
• 2. Locate the largest number and the smallest
  number. 20 and 1
• 3. Then subtract them to find the range. 20-1
  19

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Word Problem Practice

• A marathon race was completed by 5 runners.
  What is the range of times given in hours below?
   
• 2.7 hr,  8.3 hr,  3.5 hr,  5.1
  hr,  4.9 hr
• Solution  
• 1. Order the data from least to greatest.
• 2.7,  3.5,  4.9, 
  5.1,  8.3    
• 2. Subtract the highest and lowest.
• 8.3 hr - 2.7 hr 5.6
  hr
• Answer   The range of times is 5.6 hrs.

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Word Problem Practice

• On a frigid, winter day in February, the
  temperature for 8 cities in Maine was recorded.
  What is the mode of these temperatures?  
• -8,  0,  -3,  4,  12,  0,  
  -1,  0
• Solution  
• 1. Order the data from least to greatest.
•   -8,  -3,  -1,  0,  0,  0, 
  4,  12
• Count how many there are of each number. Then,
  find the most frequently occurring number.
• -8,  -3,  -1,  0,  0,  0, 
  4,  12
• Answer   The mode of these temperatures is 0.

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Word Problem Practice

• In the first 9 weeks of school, Sarahs test
  scores in math were 94, 88, 89, 78, and
  100. What is her test average (mean)?
• Solution  
• Order the data from least to greatest.
• 78, 88, 89, 94, and
  100
• Add the numbers.
• 78 88 89 94 100
  449
• Divide the total by how many there are (5).
• 449 / 5 89.8   Answer
  The mean is 89.8

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Word Problem Practice

• Jimmy's phone calls lasted 20 min., 7 min.,
  9 min., 12 min., and 8 min. He took data to show
  how long his phone calls typically were. Find the
  median value of his set of data.
• Solution  
• Order the data from least to greatest.
• 7 min., 8min., 9 min., 12
  min., and, 20 min.
• 2. Find the middle number.
• 7 min., 8min., 9 min., 12
  min., and, 20 min.
• The median is 9 min.

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Any Questions?

• Type your questions in the chat
• window please for whiteboard practice.

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Print your participant Window.

• Why? To email to your instructor as proof of
  attendance. To get 1 hour of credit towards your
  10 hours this week.
• How? Place your cursor and left click your mouse
  on the participant window. On your keyboard, hold
  down the SHIFT and PRINT SCREEN keys. Then open a
  Word document and paste (Ctrl V). Last, attach
  your word document to an email and send it to
  your instructor.

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Final Comments

• This session has been recorded for you to play
  back and view at any time.
• If you have any questions regarding this topic at
  a later time, dont hesitate to contact your
  instructor.
• Dont forget to use the Smarthinking tutor
  feature within your class site. A tutor is
  available to you 24 hours a day.

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Thank you for coming!

• I hope you will take advantage of our future
  LIVE virtual lessons and will attend some of
  those sessions as well.
• Have a great day!