Question

2 eBook Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the 3-score for each of the five observations (to 2 decimals). Enter negative values as negative numbers, Observed value -score 10 20 lllll 12 17 16

Answer 1

Q 1:

I= 75 = 15 5 n 5

Σ(x, -x) n-1 64 = 4 4

10   
Z 10-15 = -1.25 4

            

20   
20-15 Z = = -1.25 4

12   
12-15 Z = = 4 -.75

17   
17-15 = = +50 4

16   
16-15 ZE = 4 +.25
  

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​​​​​Q 2:

a.         647 is one standard deviation above the mean. Approximately 68% of the scores are between 447 and 647 with half of 68%, or 34%, of the scores between the mean of 547 and 647. Also, since the distribution is symmetric, 50% of the scores are above the mean of 547. With 50% of the scores above 547 and with 34% of the scores between 547 and 647, 50% – 34% = 16% of the scores are 647 or higher.

b.         747 is two standard deviations above the mean. Approximately 95% of the scores are between 347 and 747 with half of 95%, or 47.5%, of the scores between the mean of 547 and 747. Also, since the distribution is symmetric, 50% of the scores are above the mean of 547. With 50% of the scores above 547 and with 47.5% of the scores between 547 and 747, 50%– 47.5% = 2.5% of the scores are 747 or higher.

c.         Approximately 68% of the scores are between 447 and 647 with half of 68%, or 34%, of the scores are between 447 and the mean of 547.

d.         Approximately 95% of the scores are between 347 and 747 with half of 95%, or 47.5%, of the scores between 347 and the mean of 547. Approximately 68% of the scores are between 447 and 647 with half of 68%, or 34%, of the scores between the mean of 547 and 647. Thus, 47.5% + 34% = 81.5% of the scores are between 347 and 647.

Answer 2

0.31 right skewed

Answer 3

Z-score is 0.31 means rightly skewed.