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anonymous

  • one year ago

Which data set has the greatest spread for the middle 50% of its data? {18, 13, 22, 17, 21, 24} {17, 19, 22, 26, 17, 14} {13, 17, 12, 21, 18, 20} {18, 21, 16, 22, 24, 15}

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  1. tkhunny
    • one year ago
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    You should find the middle 50% of the data for each set.

  2. anonymous
    • one year ago
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    I figured that much on my own, why is the middle 50% though?

  3. anonymous
    • one year ago
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    *what

  4. tkhunny
    • one year ago
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    There are 6 items in each set. 50% of 6 is 3. Order the sets and pick the middle 3.

  5. anonymous
    • one year ago
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    13,17,18,21,22,24 14,17,17,19, 22,26 12,13,17,18,20,21 15,16,18, 21,22,24

  6. tkhunny
    • one year ago
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    Nicely ordered. Now pick the middle three from each.

  7. anonymous
    • one year ago
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    they each have 6 numbers, there isn't a middle three, two of them are in the middle

  8. anonymous
    • one year ago
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    @nincompoop

  9. anonymous
    • one year ago
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    @Hero

  10. tkhunny
    • one year ago
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    Well, you must decide if you will take 2 or 4. Which actually contains the middle 50%? It is a common problem with small datasets.

  11. anonymous
    • one year ago
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    so the middles would be 18, 21 17,19 17,18 and 18, 21

  12. tkhunny
    • one year ago
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    That does not contain 50%.

  13. anonymous
    • one year ago
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    huh?

  14. tkhunny
    • one year ago
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    You must use AT LEAST 50% of the data. Picking the middle 2 is only 1/3 of the data. You'll have to go up to 2/3.

  15. anonymous
    • one year ago
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    okay so the middle two are 21,22 19,22 18,20 and 21,22

  16. tkhunny
    • one year ago
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    ... and that is not helpful because you are examining only the middle 1/3. You need 1/2 AT LEAST.

  17. anonymous
    • one year ago
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    shouty capitals are not helpful, so what you mean is I need at least half of those numbers to examine?

  18. tkhunny
    • one year ago
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    It's not shouty. It's just emphasis. Perhaps a different approach. Can you find the median of each dataset?

  19. anonymous
    • one year ago
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    that I can do

  20. tkhunny
    • one year ago
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    Do you get 21.5, 20, 19, and 21.5?

  21. anonymous
    • one year ago
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    yes

  22. tkhunny
    • one year ago
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    Okay, how about the medians of the two subsets created by those medians? In other words, given {18, 13, 22, 17, 21, 24} Sorted: 13, 17,18, 21, 22, 24 Median: 19.5 Left subset: 13 17 18 ==> Median 17 Right subset 21 22 24 ==> Median 22 Make any sense?

  23. anonymous
    • one year ago
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    makes sense

  24. tkhunny
    • one year ago
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    Well, what we have just created is this list: 25th percentile = 17 50th percentile = 19.5 = Median 75th percentile = 22 Comparing the 75th to the 25th creates the "Interquartile Range". Notice how 75% - 25% = 50%. Thus, it is possible that the "middle 50% of the data" simply means the interquartile range. 22 - 17 = 5 Is this greater than or less than the interquartile range of the other sets?

  25. anonymous
    • one year ago
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    greater than

  26. tkhunny
    • one year ago
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    I believe you, but I have not calculated them. The difficulty is what is meant by "middle 50% of the data". Originally, I was interpreting that literally and it was confusing. When I decided it might just mean the Interquartile Range, we had something that could be understood and solved.

  27. anonymous
    • one year ago
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    so which set has the greatest spread

  28. tkhunny
    • one year ago
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    You tell me. Which has the greatest interquartile range? I did the first set.

  29. anonymous
    • one year ago
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    I think its b

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