In statistics we often have to compare two scores calculated using different units or scales and it is difficult to establish a comparison between these raw scores. Raw scores are the original numbers we get in a statistical experiment.
a) Z-score provide the location of a raw score relative to the mean in terms of standard deviations. In Eric’s trip the values of 1.33, -1.67 and 0 give the location of raw score relative to the mean value of 17 in terms of standard deviation e.g. a z-score of 1.33 the location of the raw score of 21 at a distance of 1.33 standard deviations from the mean of 17.
b) Z-scores also provide the location of a specific raw value relative to average standard deviation. In Eric’s trip example all z-score values can be compared to the average standard deviation 3 to deduce the location of a raw score relative to average standard deviation of the population.
c) In case of normal distribution z-scores can be used to determine the percentile scores. Percentiles can tell the percentage of the population that fall above or below a raw score. In Eric’s trip example if the sample is normally distributed than we can determine the percentage when Eric reach late to his job.
There is a close relationship between z-scores and standard normal curve. If we have a standard normal curve we can determine the relative frequencies of z-scores and raw scores, percentile rank of a raw score, a raw score based on a percentile and the population between a raw score and