Question

Consider a sample with data values of ____, ____, ____, ____, and ____. Compute the z-score for each of the five observations (to two decimals). Enter negative values as negative numbers.

Answer 1

To compute z-scores, subtract the mean from each data point and then divide by the standard deviation. The empirical rule states that about 95% of data lies within two standard deviations from the mean, corresponding to z-scores of -2 and +2.

Step-by-step explanation:

The student's question pertains to computing the z-score for each of five observations in a data sample. The z-score, also known as the standard score, measures how many standard deviations a given observation is from the mean of the dataset. To calculate the z-score for a specific data point, you subtract the mean from the data value and then divide this by the standard deviation of the dataset.

For example if we have the mean (m) and the standard deviation (σ) for a dataset, and the value (x) for which we want to calculate the z-score, the formula would be:

Z = (x - m) / σ

Referencing the information provided, a z-score of -2 corresponds to a value that is two standard deviations below the mean, and a z-score of +2 is two standard deviations above the mean. Also, it is given that about 95 percent of data values lie within two standard deviations from the mean, by the empirical rule or the 68-95-99.7 rule.