Mean, Median, and Mode

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Mean, Median, and Mode
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• In everyday life it is often important to collect
  data. Perhaps from a survey or a questionnaire.
  Once we have collected the data, it is then
  important to arrange it in a way which allows
  someone to analyze the information, so that a
  conclusion or decision can be made.

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Statistics

• 3 of the most important statistics we use when we
  analyze data are called
• The mean
• The median
• The mode

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The Mean

• The mean of a set of data is the average. To find
  the mean, add all the data values together and
  divide by the number of values.

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Lets start with an easy example!

• In her last 5 games, Sara has scored the
  following number of points
• 12, 16, 11, 17, and 18
• What is the mean of these scoring totals?

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To determine the mean, all we have to do is add
up all of her points and then divide by the
number of games she played

• 121611171874
• 74/514.8
• Saras scoring mean was 14.8 points per game

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The Median

• The median is the middle value after the data has
  been arranged in order. If the set of data
  contains an even number of values, then the
  median is the average (the mean) of the two
  middle values.

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Lets try a couple of these!

• Jake received the following test grades on his
  last 7 quizzes
• 79, 88, 75, 71, 89, 80, 92
• What was his median grade?

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• First, we must arrange the scores
• in order.
• 71, 75, 79, 80, 88, 89, 92
• In this case, we have 7 values and because 7 is
  an odd number, we have a middle number. The
  middle value will be the 4th number from either
  end of the set. In this case the median would be
  80.
• 71, 75, 79, 80, 88, 89, 92
• The median of this set is 80

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Lets do one with an even number of data values

• Over an 8 day period, Bessie, the cow, produced
  the following total gallons of milk per day
• 16, 18, 19, 15, 14, 20, 17, 22
• What was the median number of gallons over this
  period of time?

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• Again, the first step is to arrange the values in
  order
• 14, 15,16,17,18,19,20,22
• This time we have an even number of values, that
  means there is no value exactly in the middle.
  So, we have to find the average of the two middle
  numbers.
• 14, 15,16,17,18,19,20,22
• I have underlined the two middle numbers
• To average, we simply add them together and then
  divide by 2
• 171835
• 35/217.5
• The median of this set is 17.5 gallons.

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The Mode

• The mode is the data value that appears the most
  in the set. Because no value may appear more
  often than any other, it is possible for a set to
  have no mode. And because it is possible for a
  set to contain more than one element which
  appears the same number of times as another, it
  is possible for a set to have more than one mode.

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Lets look at a couple of examples

• The following is a list of heights (in inches) of
  a high school basketball team
• 68,67,66,70,74,72,68,71,75,68,72,71
• What is the mode?

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To determine the mode, all we have to do is find
which data values appear the most

• 68, 67, 66, 70, 74, 72, 68, 71, 75, 68, 72, 71
• There are 2-71s and 2-72s
• BUT, there are 3-68s
• So, the mode is 68!

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Lets look at one more

• This is a list of the grades of a class on a
  recent math test
• 85, 78, 90, 91, 88, 85, 73, 84, 90, 95, 67, 70
• Find the mode for this set of data.

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If you write the numbers in order, you will
clearly see any multiple entries.

• 67, 70, 73, 78, 84, 85, 85, 88, 90, 90, 91, 95
• This set has 2 modes 85 and 90