Measures of Central Tendency: Mean, Median, Mode and Range

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Measures of Central Tendency Mean, Median,
Mode and Range
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YOUR FOCUS

• GPS Standard M6D1cd Students will represent and
  analyze data by examining variations within and
  between groups and relating data analysis to the
  content of the question posed.
• EU We can analyze data in many ways to determine
  differences between groups.
• EQ How can I use my data to compare groups?
• Vocabulary Mean, Median, Mode, Range

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• The residents of Whateverville need your
  help! Mayor Wallop, a scientist, has invented a
  weather machine. Now he's in control of the
  weather for the entire region and has subjected
  the residents of Whateverville to so many
  different temperatures that they don't know what
  season it is. One day it's snowing the next day
  it's over 100 degrees! The plants are dying, and
  people are getting sick. Take a look at the
  temperatures in the past week.

Sunday 50
Monday 62
Tuesday 90
Wednesday 106
Thursday 10
Friday 50
Saturday 0
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• The first step to helping the residents of
  Whateverville solve this problem is to put the
  temperatures in order from least to greatest.

Sunday 50
Monday 62
Tuesday 90
Wednesday 106
Thursday 10
Friday 50
Saturday 0
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• What is the highest temperature this week?
• What is the lowest temperature this week?
• What is the difference between the highest and
  lowest temperature?

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This is your RANGE

• The range is the difference between the highest
  and the lowest numbers of the series.
• All we have to do is put the numbers in order and
  subtract the lowest from the highest!
• 106-0 106

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• Take a look at your temperatures ordered from
  least to greatest. What temperature is in the
  middle?

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This is your MEDIAN

• The Median is the middle value on the list.
• The first step is to always to put the numbers in
  order.
• 0 10 50 50 62 90
  106

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Median Example 2

• Now, lets try it with an even number of
  temperatures
• 0 10 50 50 62 90
  94 106
• This time, there are two numbers in the middle,
  50 and 62
• 0 10 50 50 62
  90 94 106
• Now we will need to find the Average of these two
  numbers, by adding them and dividing by two.
• 50 62 112 1122 56
• Here, the Median is 56

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• What is the temperature that occurs most
  frequently?

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This is your MODE

• The Mode refers to the number that occurs the
  most frequently.
• Its easy to remember the first two numbers are
  the same! MOde and MOst Frequently!
• 0 10 50 50 62 90
  106

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• How can you find the average of the temperatures?

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This is your MEAN

• The mean is the Average of a group of numbers
• It is helpful to know the mean because then you
  can see which numbers are above and below the mean

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Mean Example

• To find the Mean, first you must add up all of
  the numbers.
• 0 10 50 50 62 90 106 368
• Now, since there are 7 temperatures, we will next
  divide the sum by 7.
• 3687 52.6
• We will round to the nearest whole number.
• So, the Mean is 53

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Sunday 48 Monday 45 Tuesday 63 Wednesday
51 Thursday 101 Friday 69 Saturday
55 Sunday 62 Monday 53 Tuesday 57

• Mayor Wallop hears the complaints of the
  residents, and for the next 10 days he tries to
  adjust his temperatures to the average spring
  temperature in the region.

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• Calculate the mean, median, mode, and range for
  these new temperatures.

Sunday 48 Monday 45 Tuesday 63 Wednesday
51 Thursday 101 Friday 69 Saturday
55 Sunday 62 Monday 53 Tuesday 57
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Try this one!!!
This is the Stat Family!
Dad Mom Jack Alex Katie 34 33 5 5
1
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Mean

• Here are the ages again
• Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
• What is the Mean?
• Remember Mean is the AVERAGE
• Try it on your paper and see what you come up
  with!

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Mean

• Remember, to find the mean, we have to first add
  up all of the numbers.
• 3433551 80
• Then, since there are 6 people in the family, we
  next divide by 6.
• 786 13
• The Mean in this case is 13

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Median

• Here are the ages again
• Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
• What is the Median?
• Remember Median is the MIDDLE NUMBER
• Try it on your paper and see what you come up
  with!

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Median

• Remember, to find the mean, we have to first put
  all of the numbers in order.
• 34 33 5 5 1
• The Mean in this case is 5

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Mode

• Here are the ages again
• Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
• What is the Mode?
• Remember Mode is the MOST FREQUENT
• Try it on your paper and see what you come up
  with!

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Mode

• Remember, to find the mode, we have to first put
  all of the numbers in order.
• 34 33 5 5 1
• The Mode in this case is 5

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Range

• Here are the ages again
• Dad- 34, Mom- 33, Jack- 5, Alex- 5, Katie- 1
• What is the Range?
• Remember Range is the DIFFERENCE
• Try it on your paper and see what you come up
  with!

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Range

• Remember, to find the range, we have to first put
  all of the numbers in order.
• 34 33 5 5 1
• The highest age is 34, and the lowest is 1
• Now we need to subtract to find the difference
• 34-1 33
• The range is 33