Question

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 ⨯ 10^-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	27.46	6.74	17.10	11.92	19.32	8.96
15.25	13.40	26.72	21.17	27.83	22.65	27.46
Grid H: y variable
32.56	37.26	55.59	17.52	25.98	51.83	26.92
14.23	11.88	44.78	53.71	33.97	15.64	55.59

(a) Compute Σx, Σx²,  Σy, Σy². (Enter your answers to 2 decimal places.)

Σx		Σx2
Σy		Σy2

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Enter your answers to 2 decimal places.)

	x	y
x
s2
s

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Enter your answers to 2 decimal places.)

	x	y
Lower Limit
Upper Limit

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.

Grid H shows a wider 25% range of values.Grid E shows a wider 75% range of values.     Grid E shows a wider 25% range of values.Grid H shows a wider 75% range of values.

(d) Compute the sample coefficient of variation for each grid. (Enter your answers to one decimal place.)

	x	y
CV	%	%

Use the CV's to compare the two grids.

Grid H demonstrates greater variability per expected signal.Grid H demonstrates the same variability per expected signal as Grid E.     Grid E demonstrates greater variabiliy per expected signal.

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.

A larger CV would indicate a possibility of more buried artifacts.A larger CV would indicate the possibility of less buried artifacts.     

Answer 1

from given data

a)

Σx=	273.81	Σx2=	6077.86
Σy=	477.46	Σy2=	19654.11

b)

	x	y
x̅ =	19.56	34.10
s2	55.59	259.28
s	7.46	16.10

c)

		x	y
lower limit		4.64	1.90
upper limit		34.48	66.30

Grid H shows a wider 75% range of values.

d)

		x	y
CV		38.1%	47.2%

Grid H demonstrates greater variability per expected signal.
.A larger CV would indicate the possibility of less buried artifacts.