3. a manager records how many tasks each employee completed this week: 2, 22, 24, 25, 26, 28, 29\nshould it…

3. a manager records how many tasks each employee completed this week: 2, 22, 24, 25, 26, 28, 29\nshould it be removed? why?\nwhy? 2 is consider as an outlier, might a removal\nuse formula to check if its an outlier :\n4. a sales team logs how many units each member sold last month: 18, 19, 20, 22, 23, 25, 90\none salesperson sold 90 units, much more than the others. should this value be removed?\nwhy?\nuse formula to check if its an outlier :

3. a manager records how many tasks each employee completed this week: 2, 22, 24, 25, 26, 28, 29\nshould it be removed? why?\nwhy? 2 is consider as an outlier, might a removal\nuse formula to check if its an outlier :\n4. a sales team logs how many units each member sold last month: 18, 19, 20, 22, 23, 25, 90\none salesperson sold 90 units, much more than the others. should this value be removed?\nwhy?\nuse formula to check if its an outlier :

Answer

Explanation:

Step1: Arrange data in ascending order and find quartiles

For the first set [2, 22, 24, 25, 26, 28, 29], the median (Q2) is 25. The lower half is [2, 22, 24], so Q1 = 22. The upper half is [26, 28, 29], so Q3 = 28. For the second set [18, 19, 20, 22, 23, 25, 90], the median (Q2) is 22. The lower half is [18, 19, 20], so Q1 = 19. The upper half is [23, 25, 90], so Q3 = 25.

Step2: Calculate the Inter - Quartile Range (IQR)

For the first set, IQR = Q3 - Q1 = 28 - 22=6. The lower fence is Q1 - 1.5IQR = 22-1.56 = 13, and the upper fence is Q3 + 1.5IQR = 28 + 1.56 = 37. Since 2 < 13, 2 is an outlier. For the second set, IQR = Q3 - Q1 = 25 - 19 = 6. The lower fence is Q1 - 1.5IQR = 19-1.56 = 10, and the upper fence is Q3 + 1.5IQR = 25+1.56 = 34. Since 90>34, 90 is an outlier.

Step3: Determine if value should be removed

Outliers can skew data analysis. If the goal is to analyze typical performance (e.g., average task - completion or unit - sales of normal employees), then outliers can be removed as they do not represent the common situation. However, if the data is to represent all employees' performance without any bias, they should not be removed. In a business context where we might want to analyze normal business operations, it might be reasonable to remove them.

Answer:

For the first set with value 2: It could be removed as it is an outlier and may skew analysis of typical employee task - completion. For the second set with value 90: It could be removed as it is an outlier and may skew analysis of typical salesperson performance.