The Hill of Tara in Ireland is a place of great archaeological importance. This region has been occupied by people for more than 4000 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 1centemeter-gram-second 3 10262 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

(a) Compute ˆ‘x, ˆ‘x2, ˆ‘y, and ˆ‘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 and also for y. 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.

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27.45 13.20 5.60 16.95 23.90 Grid H: y variable 11.85 15.25 48.70 2 31.25 19.80 15.05 21.40 17.25 32.40 40.75 5.10 17.75 28.35 21.30 17.30 27.50 10.35 14.90 5.40 25.95 57.60 34.35 38.80 41.00