match each set of values to its correct number of outliers.\n185, 198, 31, 196, 549, 177, 182\n2, 7, 4, 0…

match each set of values to its correct number of outliers.\n185, 198, 31, 196, 549, 177, 182\n2, 7, 4, 0, 1, 3, 8, 5, 9, 3\n12, 14, 16, 1, 15, 15, 34, 2, 17\n48, 47, 34, 37, 11, 39\ncontains three outliers\ncontains two outliers\ncontains one outlier\ncontains no outliers

match each set of values to its correct number of outliers.\n185, 198, 31, 196, 549, 177, 182\n2, 7, 4, 0, 1, 3, 8, 5, 9, 3\n12, 14, 16, 1, 15, 15, 34, 2, 17\n48, 47, 34, 37, 11, 39\ncontains three outliers\ncontains two outliers\ncontains one outlier\ncontains no outliers

Answer

Explanation:

Step1: Recall outlier - finding method

To find outliers, we first need to find the first quartile ($Q_1$), the third quartile ($Q_3$), and the inter - quartile range ($IQR = Q_3 - Q_1$). Outliers are values less than $Q_1-1.5\times IQR$ or greater than $Q_3 + 1.5\times IQR$.

Step2: For the first set: 48, 47, 34, 37, 11, 39

Arrange in ascending order: 11, 34, 37, 39, 47, 48. The median of the lower half ($Q_1$) is 34, the median of the upper half ($Q_3$) is 47. $IQR=47 - 34=13$. $Q_1-1.5\times IQR=34-1.5\times13=34 - 19.5 = 14.5$, $Q_3 + 1.5\times IQR=47+1.5\times13=47 + 19.5 = 66.5$. The value 11 is an outlier. So it contains one outlier.

Step3: For the second set: 12, 14, 16, 1, 15, 15, 34, 2, 17

Arrange in ascending order: 1, 2, 12, 14, 15, 15, 16, 17, 34. The median of the lower half ($Q_1$) is 2, the median of the upper half ($Q_3$) is 16. $IQR = 16-2 = 14$. $Q_1-1.5\times IQR=2-1.5\times14=2 - 21=-19$, $Q_3 + 1.5\times IQR=16+1.5\times14=16 + 21 = 37$. The value 1 is an outlier. So it contains one outlier.

Step4: For the third set: 2, 7, 4, 0, 1, 3, 8, 5, 9, 3

Arrange in ascending order: 0, 1, 2, 3, 3, 4, 5, 7, 8, 9. The median of the lower half ($Q_1$) is 1.5, the median of the upper half ($Q_3$) is 7. $IQR=7 - 1.5 = 5.5$. $Q_1-1.5\times IQR=1.5-1.5\times5.5=1.5 - 8.25=-6.75$, $Q_3 + 1.5\times IQR=7+1.5\times5.5=7 + 8.25 = 15.25$. There are no values outside this range. So it contains no outliers.

Step5: For the fourth set: 185, 198, 31, 196, 549, 177, 182

Arrange in ascending order: 31, 177, 182, 185, 196, 198, 549. The median of the lower half ($Q_1$) is 177, the median of the upper half ($Q_3$) is 196. $IQR=196 - 177 = 19$. $Q_1-1.5\times IQR=177-1.5\times19=177 - 28.5 = 148.5$, $Q_3 + 1.5\times IQR=196+1.5\times19=196 + 28.5 = 224.5$. The values 31 and 549 are outliers. So it contains two outliers.

Answer:

Set 1: Contains one outlier Set 2: Contains one outlier Set 3: Contains no outliers Set 4: Contains two outliers