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

The answer is (c) {13, 17, 12, 21, 18, 20}.

Step-by-step explanation:

The given data sets are:

{18, 13, 22, 17, 21, 24},

{17, 19, 22, 26, 17, 14},

{13, 17, 12, 21, 18, 20}

and

{18, 21, 16, 22, 24, 15}.

To find the greatest spread for the middle 50%, we need to find the Interquartile range for all the data sets and check which one is highest.

For first set, Interquartile range (IQR) = 22 - 17 = 5.

For second set, IQR = 22 - 17 = 5.

For third set, IQR = 20 - 13 = 7

and

for fourth set, IQR = 22 - 16 = 6.

Since IQR is highest for the third data, so the correct option is (c)  {13, 17, 12, 21, 18, 20}.

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