A laboratory uses a light sensor that reports a constant brightness reading (in…
MATHEMATICS · Multi-part · AP · AP Statistics · Exploring Two-Variable Data · Exploring Two-Variable Data
Problem
A laboratory uses a light sensor that reports a constant brightness reading L (in lumens) during a 5–second calibration run, even though the true brightness fluctuates slightly. The true brightness was sampled once per second and recorded in the table below.
Time t (s)
0
1
2
3
4
True brightness B(t) (lumens)
502
496
500
498
504
You will model the sensor’s reading with the constant value L.
(a) Write an explicit expression S(L) for the total squared deviation between the constant model L and the observed brightness values in the table.
(b) Determine the value of L that minimizes S(L). Show all analytical work leading to your result.
(c) Interpret your result in the context of the calibration. What does the optimal value of L represent about the sensor’s behavior?