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

Explanation:

Step1: Calculate quartiles for first data - set

First, order data set ${2, 22, 24, 25, 26, 28, 29}$. There are $n = 7$ data - points. The median (second - quartile $Q_2$) is the 4th value when ordered, so $Q_2=25$. The lower half of the data is ${2, 22, 24}$, and its median (first - quartile $Q_1$) is 22. The upper half of the data is ${26, 28, 29}$, and its median (third - quartile $Q_3$) is 28. The inter - quartile range $IQR = Q_3−Q_1=28 - 22=6$. The lower fence is $Q_1−1.5\times IQR=22-1.5\times6=22 - 9 = 13$. The upper fence is $Q_3 + 1.5\times IQR=28+1.5\times6=28 + 9 = 37$. The value 2 is less than 13, so it is an outlier and may be considered for removal as it is far from the rest of the data.

Step2: Calculate quartiles for second data - set

Order data set ${18, 19, 20, 22, 23, 25, 90}$. There are $n = 7$ data - points. The median ($Q_2$) is the 4th value when ordered, so $Q_2 = 22$. The lower half of the data is ${18, 19, 20}$, and its median ($Q_1$) is 19. The upper half of the data is ${23, 25, 90}$, and its median ($Q_3$) is 25. The inter - quartile range $IQR=Q_3 - Q_1=25 - 19 = 6$. The lower fence is $Q_1−1.5\times IQR=19-1.5\times6=19 - 9 = 10$. The upper fence is $Q_3 + 1.5\times IQR=25+1.5\times6=25 + 9 = 34$. The value 90 is greater than 34, so it is an outlier. Whether to remove it depends on the context. If it is a legitimate value (e.g., a very successful salesperson), it may not be removed, but if it is due to an error, it should be removed.

Answer:

For the first data - set ${2, 22, 24, 25, 26, 28, 29}$, the value 2 is an outlier and may be considered for removal as it is below the lower fence of 13. For the second data - set ${18, 19, 20, 22, 23, 25, 90}$, the value 90 is an outlier. Whether to remove it depends on whether it is a valid data point or an error.