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The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution. 1271 1187 1194 1250 1268 1316 1275 1317 1275 (a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

User Msapkal
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1 Answer

3 votes

Answer:

The sample mean year is 1261 A.D.

The standard standard deviation is of 46 A.D.

Explanation:

Sample mean:

Sum of all values divided by the number of values. So


x = (1271+1187+1194+1250+1268+1316+1275+1317+1275)/(9) = 1261.4

Rounding to the nearest whole number, the sample mean year is 1261 A.D.

Sample standard deviation:

Square root of the sum of the difference squared between each value and the mean, divided by one less than the sample size. So


s = \sqrt{((1271-1261.4)^2+(1187-1261.4)^2+(1194-1261.4)^2+(1250-1261.4)^2+(1268-1261.4)^2+(1316-1261.4)^2+(1275-1261.4)^2+(1317-1261.4)^2+(1275-1261.4)^2)/(8)} = 45.8

Rounding to the nearest whole number, the standard standard deviation year is of 46 A.D.

User Kunal Kumar
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