5 different sailors use their sextant to measure the altitude of Polaris at 1:45 AM.

(They are all aboard the same ship)

Sailor #	measurement angle
sailor 1	30
sailor 2	30
sailor 3	50
sailor 4	50
sailor 5	60

The captain must choose a "best estimate" of the ships latitude, based on the data (the captain does not know the true angle).

a) If the captain chooses the use the angle which minimizes the mean of the absolute errors (MAD), what angle will he choose?

b) If the captain chooses the angle which minimizes the mean of the squared errors (MSE), what angle will he choose?

c) What is the standard deviation of the data set?

d) What is the z-score of Sailor 3's measurement?