Notes 2.1 (Part 1)

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Notes 2.1 (Part 1)

• Frequency distribution and their graphs

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What you should learn

• 1. How to construct a frequency distribution
  including limits, boundaries, midpoints, relative
  frequencies and cumulative frequencies.
• 2. How to construct frequency histograms,
  frequency polygons, relative frequency histograms
  and ogives.

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Frequency Distributions

• Frequency distribution is a table that shows
  classes (or intervals) of data entries, with a
  count for each class.
• f frequency (or how many times it occurs
  for a particular class)

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• Each class will have a lower class limit and an
  upper class limit.
• Lower Class Limits 45,50,55,60,65,70
• Upper Class Limits 49,54,59,64,69,74

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• Class width the distance between the lower (or
  upper) class limits of consecutive classes
• 54 49 5
• 50 45 5
• 70 65 5
• 94 89 5
• Class width is 5.
• You only have to do it one time.

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Constructing a frequency1. Decide on the
number of classes that you want to include in
your frequency distribution. (Should have
between five and 20 classes)2. Find the class
width CW Max Entry Min Entry
number of classes (Always round up to the next
whole number)3. Find the class limits. Use
min entry as lower class limit (LCL) of first
class. Find the remaining LCL by adding the
class with to each preceding class. Then find
upper class limits.
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1. Make a tally mark for each data entry in the row
   of the appropriate class.
2. Count the tally marks to find the total frequency
   ( f ) for each class.

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Step to solving

• 1. State the number of classes
• 2. Find the min and max values and the class
  width.
• 3. Find the class limits.
• 4. Tally the data entries.
• 5. Write the frequency f for each class.

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Warm Up Try it yourself 1

• Construct a frequency distribution using the ages
  of Akhiok , Alaska given below. Use six classes.
• 28, 6, 17, 48, 63, 47, 27, 21, 3, 7, 12, 39, 50,
  54, 33, 45, 15, 24, 1, 7, 36, 53, 46, 27, 5, 10,
  32, 50, 52, 11, 42, 22, 3, 17, 34, 56, 25, 2, 30,
  10, 33, 1, 49, 13, 16, 8, 31, 21, 6, 9, 2, 11,
  32, 25, 0, 55, 23, 41, 29, 4, 51, 4, 6, 31, 5, 5,
  11, 4, 10, 26, 12, 6, 16, 8, 2, 4, 28

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Assignment 12

• Construct the frequency distribution table for
  the following. (class, tally and f )
• 1. Number of rainy days in Seattle, WA during
  the last 15 years. (5 classes)
• 175, 152, 105, 201, 138, 111, 117, 142, 193, 101,
  123, 114, 164, 150, 184

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• 2. Number of victories in the last 22 years by
  the Oakland Raiders. (6 classes)
• 8, 5, 5, 4, 2, 4, 5, 4, 11, 10, 12, 8, 8, 4, 7,
  8, 9 10, 7, 9, 12, 8

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Warm Up

• Construct a frequency distribution chart with 5
  classes. The number of jobs a person has had
  before their 40th birthday.
• 2, 15, 6, 8 , 9, 10, 1, 8
• Need class, tally and frequency (if you can get
  midpoints and class boundaries).

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Notes 2.1 (Part 2)

• Midpoint, Class Boundaries, Relative Frequency
  and Cumulative Frequency

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Midpoint

• For each class you add the LCL and UCL and divide
  by 2, this gives you the midpoint for each class.
• 45 49 47
• 2

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Class Boundaries

• In order to obtain the class boundaries you
  subtract .5 from all the LCL and add .5 to all
  UCL.

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Relative Frequency

• Take the class of each frequency and divide it by
  the ? f .

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Cumulative Frequency

• You keep a running count of the frequencies.

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Notes 2.1 (Part 3)

• Graphing

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Warm-Up

• Number of accidents during the past 12 months at
  the Bristol and First Street intersection. (5
  classes)
• 14, 20, 18, 34, 17, 24, 45, 52, 37, 29 , 21, 22

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• Frequency Histogram (example on page 36)
• Bar graph
• Bars much touch
• Frequency goes on left side
• You can use either midpoints or class boundaries

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• Frequency polygon (example on page 37)
• Line graph
• Looks like a mountain
• Must use midpoints
• You add an extra midpoint to front and back of
  graph
• Frequency goes on left

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• Relative Frequency Histogram
• Bar graph
• Bars must be touching
• Must use class boundaries on the bottom
• Relative frequency goes on the left side of graph

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• Ogive (Example on page 39)
• Line graph
• Looks like your going uphill
• Must use class boundaries on the bottom of graph
• Must use cumulative frequency on the left hand
  side of graph.
• The lower class limit of the first class must
  start at zero.