which data set has an outlier?\n6, 13, 13, 15, 15, 18, 18, 22\n4, 4, 4, 8, 9, 9, 11, 18\n2, 3, 5, 7, 8, 8…

Explanation:

Step1: Calculate the inter - quartile range (IQR) for each data set

For a data set (x_1,x_2,\cdots,x_n) (sorted), the first quartile (Q_1) is the median of the lower half of the data, and the third quartile (Q_3) is the median of the upper half of the data. The inter - quartile range (IQR = Q_3 - Q_1). An outlier is a data point that is less than (Q_1-1.5IQR) or greater than (Q_3 + 1.5IQR).

Data set 1: (6,13,13,15,15,18,18,22)

• (n = 8). The lower half is (6,13,13,15), (Q_1=\frac{13 + 13}{2}=13). The upper half is (15,18,18,22), (Q_3=\frac{18+18}{2}=18). (IQR=18 - 13=5). (Q_1-1.5IQR=13-7.5 = 5.5), (Q_3 + 1.5IQR=18 + 7.5=25.5). All data points are within ([5.5,25.5]).

Data set 2: (4,4,4,8,9,9,11,18)

• (n = 8). The lower half is (4,4,4,8), (Q_1=\frac{4 + 4}{2}=4). The upper half is (9,9,11,18), (Q_3=\frac{9+11}{2}=10). (IQR=10 - 4=6). (Q_1-1.5IQR=4-9=-5), (Q_3 + 1.5IQR=10 + 9=19). The data point (18) is within ([-5,19]).

Data set 3: (2,3,5,7,8,8,9,10,12,17)

• (n = 10). The lower half is (2,3,5,7,8), (Q_1 = 5). The upper half is (9,10,12,17), (Q_3=12). (IQR=12 - 5=7). (Q_1-1.5IQR=5-10.5=-5.5), (Q_3 + 1.5IQR=12+10.5 = 22.5). The data point (2) is within ([-5.5,22.5]).

Data set 4: (3,6,7,7,8,8,9,9,9,10)

• (n = 10). The lower half is (3,6,7,7,8), (Q_1 = 7). The upper half is (8,9,9,9,10), (Q_3=9). (IQR=9 - 7=2). (Q_1-1.5IQR=7-3 = 4), (Q_3 + 1.5IQR=9+3=12). The data point (3) is less than (4).

Answer:

(3,6,7,7,8,8,9,9,9,10)