which values in this data set are outliers? 48, 52, 56, 64, 61, 20, 48, 51, 58, 48, 78 select outlier or not…

which values in this data set are outliers? 48, 52, 56, 64, 61, 20, 48, 51, 58, 48, 78 select outlier or not outlier for each value. value outlier not outlier 20 48 64 78

which values in this data set are outliers? 48, 52, 56, 64, 61, 20, 48, 51, 58, 48, 78 select outlier or not outlier for each value. value outlier not outlier 20 48 64 78

Answer

Answer:

20: Outlier 48: Not Outlier 64: Not Outlier 78: Not Outlier

Explanation:

Step1: Order the data

20, 48, 48, 48, 51, 52, 56, 58, 61, 64, 78

Step2: Find Q1 and Q3

There are 11 data - points. The median (Q2) is the 6th value, which is 52. The lower half of the data is 20, 48, 48, 48, 51. The median of the lower half (Q1) is 48. The upper half of the data is 56, 58, 61, 64, 78. The median of the upper half (Q3) is 61.

Step3: Calculate the IQR

IQR = Q3 - Q1 = 61 - 48 = 13.

Step4: Determine the outlier boundaries

Lower boundary = Q1 - 1.5IQR = 48 - 1.513 = 48 - 19.5 = 28.5. Upper boundary = Q3 + 1.5IQR = 61+1.513 = 61 + 19.5 = 80.5.

Step5: Classify the values

20 is less than 28.5, so it is an outlier. 48, 64, and 78 are within the boundaries (28.5 - 80.5), so they are not outliers.