Archaeology: Ireland The Hill of Tara in Ireland is a place of great archaeological

importance. This region has been occupied by people for more than 4,000 years.

Geomagnetic surveys detect subsurface anomalies in the earth's magnetic field. These

surveys have led to many significant archaeological discoveries. After collecting data,

the next step is to begin a statistical study. The following data measure magnetic

susceptibility (centimeter-gram-second x 10 to the power of negative 6) on two of the main grids of the Hill

of Tara (Reference: Tara: An Archaeological Survey by Conor Newman, Royal Irish

Academy, Dublin).

Grid E: x variable

27.83 20.80 17.84 38.56 13.40 30.42 34.86

34.86 21.54 11.55 8.22 29.31 31.90 18.58

Grid H: y variable

33.50 42.90 46.19 17.99 35.85 24.57 39.14

28.80 52.30 38.20 19.87 14.70 33.50 57.00

(a) Compute _x, _x2, _y, _y2.

(b) Use the results of part (a) to compute the sample mean, variance, and standard

deviation for x and for y.

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y

values. Use the intervals to compare the magnetic susceptibility on the two grids.

Higher numbers indicate higher magnetic susceptibility. However, extreme values,

high or low, could mean an anomaly and possible archaeological treasure.

(d) Compute the sample coefficient of variation for each grid. Use the CV's to compare

the two grids. If s represents variability in the signal (magnetic susceptibility)

and x represents the expected level of the signal, then s/x can be thought

of as a measure of the variability per unit of expected signal. Remember, a

considerable variability in the signal (above or below average) might indicate

buried artifacts. Why, in this case, would a large CV be better, or at least more

exciting? Explain.