Measure of Central Tendency Bonsu& Warmsley

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  • 1. Measures of central tendency
    Dominique Warmsley
    &
    Bettina Bonsu
    March 29, 2010
    Math 300-003
  • 2. When you hear someone use the word “average” to describe a set of numbers, there are 3 ways you can describe data, all of which can be thought of as “measures of central tendency”
    1. Mean
    2. Median
    3. Mode
  • 3. Mean: A set of numbers is the sum of values divided by the number of values. We can write this as a formula.
    Example:
    These are the values
    5 + 10 + 7+ 12 + 8 + 6= 48
    Add all the numbers
    Then count all the values and then divide by number of
    values.
    48 divided by 6 = 8
    So the mean for this set of values is 8
  • 4. Work It out!
    What is the Mean of this set 7,10, 8, 14, 6
    Remember: follow all the steps!
  • 5. Answer is:
    7 + 10 + 8 + 14+ 6= 45
    45 divided by 5 is ……… 9
    So your mean is 9
  • 6. Median: a middle number of a set of numbers. You have to make sure your numbers are in order first.
    Values need to be ordered least to greatest.
    If the number of data values in the list is odd, then
    the median is the middle number in the list.
    If the number of data value is even, there is no single middle
    number . So the median is the mean of the 2 middle numbers in the list.
  • 7. Watch Me!!!
    Example:
    35, 74, 53, 98, 32,
    Place in order least to greatest
    32, 35, 53, 74, 98
    The median is 53
    There are 5 values (an odd #), so the median is the middle number.
  • 8. Now I’ll watch you!
    4200, 3600, 4500, 3500, 3800
    Now put them in order, and find your
    median
  • 9. See it wasn’t that hard
    The order least to greatest
    3500, 3600, 3800, 4200, 4500
    Because there are five data values
    (an odd number) the middle number is
    median. 3800 is the median. But you knew
    that right.
  • 10. It can also look like this …..
    2600, 3900, 9800, 2200, 4100, 1500
    Next step is least to greatest
    1500, 2200, 2600, 3900, 4100, 9800
    The middle # are….. 2600, 3900
    you add both numbers 2600 + 3900 = 6500
    Then 6500 divided by 2 = 3250
    Remember these steps…….
  • 11. Now you can try this …..
    Find the median of this value set:
    26.08, 39.02, 98.07, 22.03, 41.04, 15.02
  • 12. Solution…..
    Find the median of this value set:
    26.08, 39.02, 98.07, 22.03, 41.04, 15.02
    In order from smallest to largest:
    15.02, 22.03, 26.08, 39.02, 41.04 ,98.07
    Taking the mean of the middle two values
    26.08 + 39.02= 65.1
    65.1 divided by 2= 32.55
  • 13. Mode: set of a value that occur most often.
    If two values occur most often we say the data is a bimodal.
    If more than two values occur most often, we say there is no mode.
  • 14. Data Sets
    Example1:
    6.3, 12.5, 2.3, 6.3, 1.2, 3.3, 6.3,
    The data value 6.3 appears more often
    then any number . Therefore 6.3 is the
    mode.
    Example 2:
    2, 12, 14, 67, 98, 6, 15, 13, 10
    No data value occurs most often, There is
    no mode for this set.
  • 15. Now you can try this …..
    Find the mode of the value sets :
    Pink, blue, silver, yellow, pink , blue , pink
    6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 2
    2, 5, 10, 3, 6, 19, 11, 20, 19
  • 16. Solution……
    Find the mode of the value sets :
    Pink, blue, silver, yellow, pink , blue , pink
    Mode is: pink
    6, 14, 13, 12, 14, 6, 5, 6, 10, 14, 2
    Bimodal sets are: 6, 14
    2, 5, 10, 3, 6, 9, 11, 20, 19
    Mode is: none
  • 17. Food For Thought!
    So, remember when you think average,
    think a set a numbers .
    And revisit your friends :
    Mean
    Median
    Mode
    Remember math is your friend !
    Give him a hug