The document describes the calculation of z-scores for a sample dataset consisting of values 10, 20, 12, 17, and 16. It outlines the steps taken to compute the mean and standard deviation which are used to derive the z-scores for each observation. The final z-scores calculated for the observations are -1.25, 1.25, -0.75, 0.5, and 0.25, respectively.

1. Consider a sample with data values of 10, 20, 12, 17, and 16.Compute the z-score for each of the
five observations (to2 decimals).
Observed valuez-score1020121716
Solution
mean = (10+20+12+17+16)/5=15
standard deviation = 4 (based on the data)
Z-score = (X-mean)/standard deviationObserved ValueZ-score10(10-15)/4 =-1.2520(20-
15)/4=1.2512(12-15)/4=-0.7517(17-15)/4=0.516(16-15)/4=0.25