Answer: 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 se, so the correct option is (c) {13, 17, 12, 21, 18, 20}.
