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

30.79 12.66 15.99 33.01 37.82 6.37 38.19

29.31 10.81 38.93 15.99 13.77 13.77 27.09

Grid H: y variable

30.68 17.05 56.53 43.84 56.06 13.29 50.89

32.56 36.79 41.02 56.53 30.68 13.76 38.20

(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.)

the mean for both E and H

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

Answer 1

(b)

Following table shows the calculations:

	X	Y	(x-mean)^2	(y-mean)^2
	30.79	30.68	57.9121	39.8161
	12.66	17.05	110.6704	397.6036
	15.99	56.53	51.6961	381.8116
	33.01	43.84	96.6289	46.9225
	37.82	56.06	214.3296	363.6649
	6.37	13.29	282.5761	561.69
	38.19	50.89	225.3001	193.21
	29.31	32.56	37.5769	19.6249
	10.81	36.79	153.0169	0.04
	38.93	41.02	248.0625	16.2409
	15.99	56.53	51.6961	381.8116
	13.77	30.68	88.5481	39.8161
	13.77	13.76	88.5481	539.6329
	27.09	38.2	15.2881	1.4641
Total	324.5	517.88	1721.85	2983.3492

Sample size: n=14

Mean:

Standard deviation:

The variance is:

(c)

According to Chebyshev theorem, 75% data values lies within 2 standard deviations of mean.

For x:

Lower limit: 0.16

Upper limit: 46.20

For y:

Lower limit: 6.69

Upper limit: 67.29