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Choosing the "best" measure of center

Mean and median both try to measure the "central tendency" in a data set. The goal of each is to get an idea of a "typical" value in the data set. The mean is commonly used, but sometimes the median is preferred.

Part 1: The mean

A golf team's 6 members had the scores below in their most recent tournament:
70, comma, 72, comma, 74, comma, 76, comma, 80, comma, 114
problem a
Calculate the mean score.
mean =
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

problem b
What is a correct interpretation of the mean score?
Choose 1 answer:
Choose 1 answer:

Part 2: The median

problem a
Find the median score.
As a reminder, here are the scores: 70, comma, 72, comma, 74, comma, 76, comma, 80, comma, 114
median =
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

problem b
What is a correct interpretation of the median score?
Choose 1 answer:
Choose 1 answer:

Part 3: The "best" measure of center

Which measure best describes the scores of the team?
As a reminder, here are the scores: 70, comma, 72, comma, 74, comma, 76, comma, 80, comma, 114
The
best describes the scores of the team, because the
is higher than almost all of the scores in the data set.

Want to join the conversation?

  • piceratops ultimate style avatar for user julius
    What if there would be more same scores, lets say : 70, 70, 70, 75 , 80 , 90, 120.
    The mean would be best to describe?
    (3 votes)
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    • duskpin ultimate style avatar for user Maya B
      If the scores were closer together and not skewed by an outlier (so the data is symmetrical), then the mean is the best measure of center to use to describe the data. Since the data is skewed by an outlier, then the median is the best measure of center to use to describe the data set.
      (3 votes)
  • piceratops seed style avatar for user jesiah.mack
    How can you tell what the median is if the is two numbers in the middle?
    (16 votes)
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  • piceratops seed style avatar for user arturop3gonzalez
    When there is an outlier, which measure of center is better to choose (mean or median)
    (10 votes)
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  • blobby green style avatar for user sabahmubarak5
    Please can someone help me with this problem it says:
    A set of data has 10values no two of which are the same if the smallest value is removed from the set . Which of these statements must be true.
    - the range of the first data set is greater than the range of the second data set.
    - the mode of the first data set is greater than the mode of the second data set.
    -the medians of the two data sets are the same .
    - the mean of the first data set is greater than the mean of the second data set.
    (10 votes)
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    • aqualine ultimate style avatar for user Timber Lin
      your original set could be: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
      your new set is now: 2, 3, 4, 5, 6, 7, 8, 9, 10

      -the first data set's range is greater (9>8).
      -neither set has a mode
      -second data set's median is greater (6>5.5)
      -2nd data mean is greater: (2+3+4+5+6+7+8+9+10)/9=6
      (1+2+3+4+5+6+7+8+9+10)/10=5.5
      (7 votes)
  • blobby green style avatar for user 1947BarBara77
    How do you determine the mean and mode when the data set of numbers is too big to visualize individually?
    (8 votes)
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  • blobby green style avatar for user 1315047620
    When you find the median and its 2 numbers like 75 and 68 how do you find the middle? Would you put them from least to greatest, add then divide by 2?
    (6 votes)
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  • male robot johnny style avatar for user Riley Chaffin
    Say if there was 69,69,69,69,69.72,80 would that mean that the mode would be the best measure of center because 69 is over half of the data so it would make sense for it to be the mode. Or would it not make sense?
    (4 votes)
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  • blobby green style avatar for user bryan
    because the sun is far oway when a ubject is far and a small ubject that when you line it up the small ubject blocks the bigger.
    (4 votes)
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  • blobby green style avatar for user briannameza21
    For the best measure of center #3 I don't get how the median best describes the score?
    (4 votes)
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  • stelly blue style avatar for user advithi01
    It says the mean is higher than all the scores but the mean is 81 and the highest score is 114. How is it higher than all the scores?
    (3 votes)
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