Question

1. a manager records how many sales each employee completed this week. 12, 22, 24, 15, 18, 28, 20 should it be removed? why? 2. 18 is an outlier, might consider as a removal. use formula to check if it is an outlier: 4. a sales team logs how many units each member sold last month. 18, 13, 20, 22, 23, 25, 90 one salesperson sold 90 units, much more than the others. should this value be removed? 90 is an outlier and might considered. use formula to check if it is an outlier:

Explanation:

Step1: Arrange data in ascending - order and find quartiles

For the first set of data [12, 15, 18, 22, 24, 26, 29], the number of data points $n = 7$. The median (second - quartile $Q_2$) is the 4th value when ordered, so $Q_2=22$. The lower half of the data is [12, 15, 18], and its median (first - quartile $Q_1$) is 15. The upper half of the data is [24, 26, 29], and its median (third - quartile $Q_3$) is 26.

Step2: Calculate the inter - quartile range (IQR)

$IQR = Q_3 - Q_1=26 - 15 = 11$.

Step3: Determine the lower and upper bounds for non - outliers

Lower bound $=Q_1-1.5\times IQR=15 - 1.5\times11=15 - 16.5=- 1.5$. Upper bound $=Q_3 + 1.5\times IQR=26+1.5\times11=26 + 16.5 = 42.5$. Since 12 is within the bounds, it should not be removed.

For the second set of data [13, 15, 20, 22, 23, 25, 90], $n = 7$. The median ($Q_2$) is 22. The lower half is [13, 15, 20], so $Q_1 = 15$. The upper half is [23, 25, 90], so $Q_3 = 25$.

Step4: Calculate the IQR for the second set

$IQR=Q_3 - Q_1=25 - 15 = 10$.

Step5: Determine the lower and upper bounds for non - outliers for the second set

Lower bound $=Q_1-1.5\times IQR=15 - 1.5\times10=0$. Upper bound $=Q_3 + 1.5\times IQR=25+1.5\times10=40$. Since 90 is greater than 40, it is an outlier. Whether to remove it depends on the context. If it is a valid data point (e.g., a very successful salesperson), it should not be removed; if it is due to an error (e.g., data entry error), it can be removed.

Answer:

For the first set, 12 should not be removed as it is within the non - outlier bounds. For the second set, 90 is an outlier. Whether to remove 90 depends on the context (valid data or error).