MAT 150 Unit 22

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MAT 150 Unit 22

• Ch 6 1 and 6 2
• Interpreting and Analyzing Data

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Section 6 1 Reading Circle, Bar and Line Graphs

• Circle Graphs (aka Pie Charts) used to show how
  a whole quantity is divided into parts.
• Sum of the parts whole quantity
• Can be represented as values, percents, fractions
  or decimals

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Section 6 1 Reading Circle, Bar and Line Graphs
Distribution of wholesale price of 425 Color TV
Overhead80
Labels
Tariff40
Title
Profit50
Material125
Labor130

• Examine the title to see what information is
  shown
• Examine the parts to see how they relate to the
  whole
• Examine the labels for each part to see what the
  part is.

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Section 6 1 Reading Circle, Bar and Line Graphs

• Bar Graph (aka Histogram) used to compare
  amounts.
• Can be drawn vertically or horizontally
• Has axis or reference lines that run alongside
  the bars to scale or measure the amounts shown.

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Section 6 1 Reading Circle, Bar and Line Graphs
Company Oil Production
1980 1985 1990 1995 2000 2005
Title
0 1 2 3 4 5
6 100 Million Barrels
Label
Axis or scales
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Section 6 1 Reading Circle, Bar and Line Graphs

• Line Graph used to show changes in data.
  Usually the horizontal axis represents some
  period of time while the vertical axis represents
  numerical amounts.

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Section 6 1 Reading Circle, Bar and Line Graphs
Average Daily Temp. in Tampa, FL
Fo
90 85 80 75 70 65 60 55
Title
Scales
J F M A M J J A S O N D
Labels
Months
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Section 6 2Measures of Central Tendency

• Average an approximate number that is a central
  value of a set of data. Used to describe
  performance or predict outcome.
• Mean
• Median
• Mode

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Section 6 2Measures of Central Tendency

• Mean
• What you would normally think of as the average.
• Sum the quantities
• Divide by the number of quantities
• Ex. 1 Find the mean of 22, 31, and 37
• Sum is 22 31 37 90
• There are three quantities so divide 90/3 30.
  
• So 30 is the mean or average of this data set.

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Section 6 2Measures of Central Tendency

• Median
• The midpoint or middle quantity in a group of
  numbers
• Arrange values in order, either descending or
  ascending.
• If there are an odd number of values, the median
  is the middle value
• If there are an even number of values, the median
  is the average (mean) of the two middle values.

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Section 6 2Measures of Central Tendency

• Median Example 1
• Recorded pulse rates at Dr. Xi were
• 68, 88, 76, 64 and 72
• Arrange in order 64, 68, 72, 76, 88
• Since there are an odd number (5) of pulse rates
  the median is the middle score.
• 64, 68, 72, 76, 88

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Section 6 2Measures of Central Tendency

• Median Example 2
• Recorded pulse rates at Dr. Yu were
• 90, 68, 88, 76, 64 and 72
• Arrange in order 64, 68, 72, 76, 88, 90
• Since there are an even number (6) of pulse rates
  the median is the average of the two middle
  scores.
• 64, 68, 72, 76, 88, 90
• (72 76)/2 74

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Section 6 2Measures of Central Tendency

• Mode the most frequently occurring value in the
  data set. To find the mode
• Identify the value or values that occur the most.
• If no value occurs more than another there is no
  mode for that data set.
• If more than one value occurs with the greatest
  frequency, they are all modes.

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Section 6 2Measures of Central Tendency

• Mode examples
• Tips for a server at a local restaurant were as
  follows 5.00, 3.00, 12.25, 5.00, 6.25, 3.75,
  5.00, 10.00, 8.65, 5.00
• Since 5.00 occurs 4 times, the mode is 5.00

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Section 6 2Frequency Distribution

• For a class of 25 students the following grades
  were recorded
• 76 91 71 83 97 87 77 88 93 77
  93 81 63
• 79 74 77 76 97 87 68 90 84 88
  91 89
• It can be difficult to make sense out of the
  grades as they appear here. They can, however,
  be grouped into smaller groups, called class
  intervals. Here class means special category.
  The scores can be grouped in intervals of 5, 7,
  9, etc, scores. Use an odd number so the middle
  score is the class midpoint.

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Section 6 2Frequency Distribution

• This is done through a frequency table

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Section 6 2Frequency Distribution

• From the grouped data the following questions can
  be answered more easily
• How many students scored 70 or above?
• 2 6 3 5 5 2 23
• How many students made an A (90 or higher)?
• 5 2 7
• What percent of the total grades were As?
• 7 As / 25 total 7/25 0.28 28
• What is the ratio of As to Fs?
• 7 As/2 Fs 7/2
• Were the students prepared for the test?
• Yes, given the high ratio of As to Fs

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Section 6 2Frequency Distribution

• Finding the mean of grouped data
• The mean of the grouped data is 2070/25 82.8