Measures of Central Tendency and Range

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Measures of Central Tendency and Range

• Choosing Measures of Central Tendency or Range to
  Describe a Set of Data and Justifying the Choice
  for a Particular Situation (TEKS 7.12A and B)

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• What do Measures of Central Tendency show us?
• Numbers or pieces of data that can represent the
  whole set of data

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• What are Measures of Central Tendency?
• Mean
• The arithmetic average of the set of data.
• The most common measure of central tendency.
• Median
• The median is the middle score in a set of data.
  
• Half the data will be above the median, and half
  below when data is ordered.
• Mode
• The mode is the most frequently occurring value
  or most popular choice

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• Consider the following math student
• John Doe has gotten the following grades on
  homework
• 96 94 90 100 86 91
  88 100 0 96 96
• Without calculating what type of student do you
  think John Doe is? (A student, B student, etc.)
• It appears that John is an A student

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• Grades
• 96 94 90 100 86 91
  88 100 0 96 96
• Find the mean, median, and mode of the grades
• Mean about 85
• Median 94
• Mode 96
• What caused Johns mean (average) to be an 85
  instead of the A that we expected?

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Pros and Cons

• Pros
• Mean
• Most familiar measure
• Uses all the data
• Median
• Not affected by extreme values
• Easy to compute
• Always exists
• Mode
• Easiest to find
• Not affected by extreme values
• Good for categorical data
• Doesnt always exist

• Cons
• Mean
• Affected by extreme values (very high or very
  low)
• Median
• Doesnt use all data values
• Data must be properly ordered
• Mode
• Doesnt use all data values
• Not always descriptive of entire data set
• Not necessarily unique

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Strategies to Choose the Appropriate Measure of
Central Tendency

• Order the data first to make it easier to find
  the median and mode.
• Look for outliers (numbers that are a lot higher
  or lower than the rest of the set an extreme
  value) they affect the mean the most!
• Is the data numerical or categorical (words)?
• Start with the easiest mode, then median, then
  mean. You may find you dont need to work out
  all of them.

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Using Measures of Central Tendency and Range to
find Missing Data

• Identify which measure of central tendency you
  are given or if the range is given.
• Mode Check to see if the mode of the data in
  the table and the mode given are the same.
• Median Put the median given in the middle and
  order the data around it.
• Range Are you missing the highest or the lowest
  piece of data?
• Mean work backwards.

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Answer the following using the strategies you
have developed.
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The table below is a list of past Super Bowl
games, the champion teams, and the defeated teams.
Super Bowl Champion Team Defeated Team
XLIII (2009) Pittsburg, 27 Arizona, 23
XLII (2008) New York, 17 New England, 14
XLI (2007) Indianapolis, 29 Chicago, 17
XL (2006) Pittsburg, 21 Seattle, ___
XXXIX (2005) New England, 24 Philadelphia, 21
XXXVIII (2004) New England, 32 Carolina, 29
XXXVII (2003) Tampa Bay, ___ Oakland, 21
XXXVI (2002) New England, 20 St. Louis, 17
Tampa Bay was the highest scoring team in the
years listed. The range of the scores of the
champion teams is 31. What was Tampa Bays score?
Seattle was the lowest scoring team in the years
listed. The range of the scores of the defeated
teams is 19. What was Seattles score?
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Patrice records the number of calories she burns
while exercising each day, as shown below. Day
1 250 calories Day 2 350 calories Day 3 400
calories Day 4 250 calories Day 5 300
calories How many calories must Patrice burn on
the sixth day to have a mean of 300
calories burned for the 6 days? F 0 calories G
150 calories H 250 calories J 310 calories
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Randy and his 5 friends played a card game in
which the person with the lowest final score
wins. The table below shows the final scores for
all the players except Erica. If Erica
won the game and the range of the scores was 17,
what was Ericas score? F 104 G 106 H 140 J 124
Player Score
Randy 121
Erica
Jon 119
Sam 107
Dawn 123
Maya 112