Question

The data set represents the number of rings each person in a room is wearing.0, 2, 4, 0, 2, 3, 2, 8, 6 What is the interquartile range of the data?

Answer 1

Answer:

IQR = 2

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Step-by-step explanation:

The interquartile range (IQR) is the difference between the third and first quartiles:  IQR = Q₃ - Q₁

To get the quartiles, we essentially cut the data into quarters:

1. Sort the data.  0th and 4th quartiles (Q₀ and Q₄) are min and max.
2. Cut in half.  The middle term is the median.  This is the 2nd quartile (Q₂).  [ If you have an even number of data items, there isn't a middle term, so use the average of the two middle terms. ]
3. Cut each half in half.  The middle terms from each half are the 1st and 3rd quartiles (Q₁ and Q₃).

Doing those steps with our data:

1.  0, 0, 2, 2, 2, 3, 4, 6, 8     Q₀ = min = 0.    Q₄ = max = 8
2.  0, 0, 2, 2, 2, 3, 4, 6, 8      The median.   Q₂ = 2
3.  0, 0, 2, 2, 2, 3, 4, 6, 8      Q₁ = 2.     Q₃ = 4

Now we can say the interquartile range is

IQR = Q₃ - Q₁ = 4 - 2 = 2