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.