You measure the total Earth\'s magnetic field using the magnetometer app of your
ID: 1331574 • Letter: Y
Question
You measure the total Earth's magnetic field using the magnetometer app of your smart phone. Assume only random noise and no systematic errors. You make 12 measurements in total with values of H = 53.3, 53.7, 53.2, 54.1, 54.7, 55.0, 53.2, 53.3, 53.0, 52.9, 53.4, 53.2 mu T. (You can use these values, or take your own data with your phone). Calculate the mean, the standard deviation, and the standard error of the mean (use corresponding function of the calculator or Mathematica). Report the result in standard format. Research the value for the Earth's magnetic field in Boulder here: http://geomag.usgs.gov/map/. What is the variation (max and min value) within the last 12 hours? Does your value agree within the uncertainty with the field in Boulder of that 12 hour period?Explanation / Answer
a)
Mean = (53.3+53.7+53.2+54.1+54.7+55+53.2+53.3+53+52.9+53.4+53.2)/12 = 53.6 uT
Variance = ((53.3-53.6)^2+(53.7-53.6)^2+(53.2-53.6)^2+(54.1-53.6)^2+(54.7-53.6)^2+(55-53.6)^2+(53.2-53.6)^2+(53.3-53.6)^2+(53-53.6)^2+(52.9-53.6)^2+(53.4-53.6)^2+(53.2-53.6)^2)/12
= 0.415
So, standard deviation = sqrt(variance) = sqrt(0.415) = 0.644