PART I

$($Use this information to answer questions $1-5.)$ The Distribution Center Manager of a leading e$-$commerce retailer has measured the

productivity of the three shifts that work in the Packaging Department. Shift One works from $7$:$00$am to $3$pm; Shift Two works from

$3$:$00$pm to $11$:$00$pm; and Shift Three works from $11$:$00$pm to $7$:$00$am$.$ The three shifts work Monday thru Saturday. The Manager

measures shift productivity by the total number of packages completed per shift per week. For the past $8$ weeks, he has compiled

the following statistics on packages completed per shift per week. $($Each question for this problem is worth one point.$)$

Packages Completed Per Shift$/$Week

The mean packages completed per shift per week for Shift One, Shift Two,

and Shift Three, respectively, are:

a$.2125\mathrm{.}0,2100\mathrm{.}0,2025\mathrm{.}0$

b$.2062\mathrm{.}5,2106\mathrm{.}25,2031\mathrm{.}25$

c$.2100\mathrm{.}0,1950\mathrm{.}0,2000\mathrm{.}0$

d$.2250\mathrm{.}0,1950\mathrm{.}0,2000\mathrm{.}0$

The median packages completed per shift per week for Shift One, Shift Two,

and Shift Three, respectively, are:

a$.2125\mathrm{.}0,2100\mathrm{.}0,2025\mathrm{.}0$

b$.2062\mathrm{.}5,2106\mathrm{.}25,2031\mathrm{.}25$

c$.2100\mathrm{.}0,1950\mathrm{.}0,2000\mathrm{.}0$

d$.2250\mathrm{.}0,1950\mathrm{.}0,2000\mathrm{.}0$

The mode of packages completed per shift per week for Shift One, Shift Two,

and Shift Three, respectively, are:

a$.2125\mathrm{.}0,2100\mathrm{.}0,2025\mathrm{.}0$

b$.2062\mathrm{.}5,2106\mathrm{.}25,2031\mathrm{.}25$

c$.2100\mathrm{.}0,1950\mathrm{.}0,2000\mathrm{.}0$

d$.2250\mathrm{.}0,1950\mathrm{.}0,2000\mathrm{.}0$

Which week contains a data "outlier" for Shift One?

a$.$ Week $1$

b$.$ Week $3$

c$.$ Week $5$

d$.$ Week $8$

In computing the relative productivity of the three shifts, what should the manager do about

the "outlier" data point in Shift One?

a$.$ Eliminate it from his calculations of central tendency for Shift One.

b$.$ Eliminate the entire week from the central tendency calculations of all three shifts.

c$.$ Investigate the reason for the "outlier" before making any decision to keep or eliminate i

d$.$ Include it in Shift One's central tendency calculations regardless of the cause for it$.$