Central Tendency

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Central Tendency Range
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Central Tendency

• Central Tendency is a value that describes a
  data set.

Mean, Median, and Mode are the measures of
Central Tendency.
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Definition

•  The MEAN is found by taking the sum of the data
  and dividing the sum by the total number of
  values in the set.
• The mean is the AVERAGE

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Example 1

• Find the mean swimming time (in minutes) rounded
  to the nearest tenth  
• 2.6 7.2 3.5 9.8 2.5
• The mean swimming time to the nearest tenth is
  5.1 minutes.

2.6 7.2 3.5 9.8 2.5 25.6
25.6 5 5.12
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Example2

• Giadas Science test scores were 95, 82, 91, and
  90. What does she need to get on her next test
  to have an average of 90 in Science?  

92
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Definition

• The median is the middle number in the set.
• Calculate the median by listing the data in order
  from least to greatest.
• The median is the MIDDLE

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Example 1

• During the first marking period, Nicks quiz
  scores were 90, 92, 93, 88, 95, 88, 97, and 87.
  What was the median score?
• What if there are two middle numbers?

Order the ages from least to greatest 87, 
88,  88,  90,  92, 93, 95, 97
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(continued)
Since there is an even number of items in the
data set, we compute the median by taking the
average of the two middle numbers.

• The median quiz score was 91.

90 92 182
182 2 91
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Example 2

• Find the median swim times (in minutes) 2.6,
  7.2, 3.5, 9.8, 2.5

3.5 minutes
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Definition

• The mode is the number (or numbers) that appear
  most often.
• It is easier to find the mode when numbers are
  listed in order.
• The mode is the MOST

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Example1

• The number of points scored in a series of
  football games is listed below. Which score
  occurred most often?  
• 7,  13,  18,  24,  9,  3,  18
• The score which occurs most often is 18.

Order the ages from least to greatest 3,  7,
9,  13,  18,  18, 24
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Example 2

• A marathon race was completed by 5 participants.
  What is the mode of these times given in hours?
   
• 2.7 hr,  8.3 hr,  3.5 hr,  5.1 hr,  4.9 hr

Since each value occurs only once, there is no
mode for this data set.
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Example 3

• 11 cars were tested in crash tests to find what
  impact speed would cause the least damage. Find
  the mode of the speeds (in mph) given  
• 24,  15,  18,  20,  18,  22,  24,  26,  18,  26, 
  24

• List in Order
• 15,  18,  18,  18,  20,  22,  24,  24,  24,  26, 
  26

Since both 18 and 24 occur three times, the modes
are 18 and 24 miles per hour.
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Definition

• The range of a set of data is the difference
  between the highest and lowest values in the set.
  
• The range is NOT a measure of Central
  Tendency

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Example1

• The Smith family drove through six Midwestern
  states on their summer vacation. Gasoline prices
  varied from state to state. What is the range of
  gasoline prices?
• 1.79,  1.61,  1.96,  2.09,  1.84,  1.75
• The range of the gasoline prices was 0.48.

2.09 - 1.61 0.48
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Example2

• Find the range of the swim times (in minutes)
  2.6, 7.2, 3.5, 9.8, 2.5

7.3 minutes
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Try the following problem

• Find the mean, median, mode, range of the test
  scores below. Determine the best measure of
  Central Tendency
• 79,  54,  87,  86,  88,  91
• Mean 80.8 Median 86.5
• Mode NONE Range 37

Best Measure of Central Tendency Median
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An outlier is an extreme value that greatly
affects the data set. The measure of
Central Tendency that is most affected by an
outlier __the mean___
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• Students in Mrs. Longs Tan Class surveyed their
  class of 25 students to determine each students
  height in inches.
• Calculate each measure of central tendency
• Mean
• Mode
• Median

61.16
65
61
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Now that was easy!