A small municipality recorded the total gallons of potable water used each day for…
MATHEMATICS · Multi-part · AP · AP Statistics · Exploring Two-Variable Data · Exploring Two-Variable Data
Problem
A small municipality recorded the total gallons of potable water used each day for one week, shown in the table below.
Day: Mon Tue Wed Thu Fri Sat Sun
Usage (10^3 gal): 44.2 46.1 43.5 45.0 48.3 51.7 47.2
City planners wish to announce a single daily‐allocation value A (in thousands of gallons) that best represents the entire week’s usage. The value of A will be chosen to minimize the total squared deviation between A and the recorded daily usages.
(a) Write an explicit expression S(A) for the total squared deviation between the allocation A and the seven recorded daily usages.
(b) Determine the value of A that minimizes S(A). Show all analytic work leading to your answer.
(c) Verify that the value of A found in part (b) indeed yields a minimum of S(A).
(d) Give a practical interpretation of the minimizing value of A in the context of the city’s announcement.