# sd02 1o1 a18. | Archaeology: Ireland The Hill of Tara in Ireland is a place of great ar-chaeological importance. This region has been occupied by people forbmore than 4000 years. Geomagnetic surveys detect subsurface anomaliesin the earth's magnetic field. These surveys have led to many significantarchaeological discoveries. After collecting data, the next step is to begina statistical study. The following data measure magnetic susceptibility(centimeter-gram-second X 10-)(Reference: Tara: An Archaeological Survey by Conor Newman, Royal IrishAcademy, Dublin).00g shO band brO9dmnnlisnUOB0U Eronb oubeomsis oabood basbt bobboul Isnutotwo of the main grids of the Hill of Tara927am baoTedbohg101 Diot sinGrid E: x variable13.205.6019.8015.0521.4017.2527.45TOA116.95 23.90 32.4040.755.1017.7528.35021Grid H: y variable11.8515.2521.3017.3027.5010.3514.90bauw to48.7025.4025.9557.6034.3538.8041.0031.25(a) Compute 2x, E, 2y, and y(b) Use the results of part (a) to compute the sample mean, variance, andstandard deviation for x and for y(c) Compute a 75% Chebyshev interval around the mean for x values and01 also for y values. Use the intervals to compare the magnetic susceptibilityon the two grids. Higher numbers indicate higher magnetic susceptibility.However, extreme values, high or low, could mean an anomaly and pos-sible archaeological treasure.(d) Interpretation Compute the sample coefficient of variation for eachgrid. Use the CVs to compare the two grids. If s represents variabilityy.1 ND VARIATIONin the signal (magnetic susceptibility) and x represents the expectedlevel of the signal, then s/x can be thought of as a measure of thevariability per unit of expected signal. Remember, a considerablevariability in the signal (above or below average) might indicate bur-ied artifacts. Why, in this case, would a large CV be better or at leastmore exciting? Explain.

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Step 1

Note:

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Step 2

(a).

Compute ∑x, ∑x2, ∑y, ∑y2.

 x y x^2 y^2 13.2 11.85 174.24 140.4225 5.6 15.25 31.36 232.5625 19.8 21.3 392.04 453.69 15.05 17.3 226.5025 299.29 21.4 27.5 457.96 756.25 17.25 10.35 297.5625 107.1225 27.45 14.9 753.5025 222.01 16.95 48.7 287.3025 2371.69 23.9 25.4 571.21 645.16 32.4 25.95 1049.76 673.4025 40.75 57.6 1660.563 3317.76 5.1 34.35 26.01 1179.923 17.75 38.8 315.0625 1505.44 28.35 41 803.7225 1681 31.25 976.5625 ∑x= 284.95 ∑y =421.5 ∑x2=7046.798 ∑y2=14562.29
Step 3

(b).

Compute the sample mean, variance and standard deviatio...

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