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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?


2

3

4

6

Verified Answer :

d1,..,d9 = 0,0,2,2,2,3,4,6,8  //there are 9 values, in ascending order
Q2 (median) = d5 = 2  //value in the middle
Q1 = (d2+d3) / 2 = (0+2)/2 = 1
(Q1 is middle value of d1,d2,d3,d4, but there is no middle element among four elements, that is why arithmetic mean is taken)
Q3 = (d7+d8) / 2 = (4+6)/2 = 5
interquantlie range = IQR = Q3 - Q1 = 5 -1 = 4
answer: 4

Answer:

Option C.

Step-by-step explanation:

The given data set is

0, 2, 4, 0, 2, 3, 2, 8, 6

Arrange the data in ascending order.

0, 0, 2, 2, 2, 3, 4, 6, 8

Divide the data set in 4 equal parts.

(0, 0), (2, 2), 2,( 3, 4), (6, 8)

Now, we get

\(Q_1=\dfrac{0+2}{2}=1\)

\(Q_2=Median=2\)

\(Q_3=\dfrac{4+6}{2}=5\)

The interquartile range formula:

\(IQR=Q_3-Q_1\)

\(IQR=5-1\)

\(IQR=4\)

The interquartile range of the data is 4. Therefore, option C is correct.

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