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(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are  z3 ≈ −1.101, z4 ≈ −0.944, z9 ≈ −0.157, z14 ≈ 0.629, and z20 ≈ 1.573.  Find the mean and the standard deviation of these z-scores. mean       standard deviation

(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are  z3 ≈ −1.101, z4 ≈ −0.944, z9 ≈ −0.157, z14 ≈ 0.629, and z20 ≈ 1.573.  Find the mean and the standard deviation of these z-scores. mean       standard deviation

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are 

z3 ≈ −1.101,
z4 ≈ −0.944,
z9 ≈ −0.157,
z14 ≈ 0.629,
and z20 ≈ 1.573.

 Find the mean and the standard deviation of these z-scores.

mean      
standard deviation 

 

(b) The population 2, 6, 12, 17, 22, and 25 has a mean of 14 and a standard deviation of 8.226. The z-scores for each of the six data values are 

z2 ≈ −1.459,
z6 ≈ −0.973,
z12 ≈ −0.243,
z17 ≈ 0.365,
z22 ≈ 0.973,
and z25 ≈ 1.337.

 Find the mean and the standard deviation of these z-scores.

mean      
standard deviation  

(c) Use the results of part (a) and part (b) to make a conjecture about the mean and standard deviation of the z-scores for any set of data.

 
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