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10. If x-8, x-6, 6, 8, 10, x+2, 14 are in ascending order and its third quartile is 12, find its first quartile.​

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Answer: 4

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Step-by-step explanation

Let's label the 7 items A,B,C,D,E,F,G

  • A = x-8
  • B = x-6
  • C = 6
  • D = 8
  • E = 10
  • F = x+2
  • G = 14

The middle most value (aka median) is D = 8

Split the set into the two subsets {A,B,C} and {E,F,G} to represent the stuff below the median and above the median respectively.

B and F are the medians of those subsets, and they represent the first quartile (Q1) and third quartile (Q3) in that order.

We're told Q3 = 12, so,

F = 12

x+2 = 12

x = 12-2

x = 10

We can update the values to:

  • A = x-8 = 10-8 = 2
  • B = x-6 = 10-6 = 4
  • C = 6
  • D = 8
  • E = 10
  • F = x+2 = 10+2 = 12
  • G = 14

Or in short

  • A = 2
  • B = 4
  • C = 6
  • D = 8
  • E = 10
  • F = 12
  • G = 14

We have the set {2,4,6,8,10,12,14} which has B = 4 as the first quartile.

You can use a quartile calculator to confirm the answer is correct.

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