Q. Determine Z-scores and Percentiles?

Ans.

Z-scores help measure how far a piece of data is from the mean. More specifically, Z-scores tell how far a piece of data is from the mean in terms of standard deviations. For example, if a data set has a mean of 30 and a standard deviation of 5, then a data value of 45 has a z-score of 3 because it is three standard deviations above the mean. Similarly, a data value of 20 has a z-score of 2 because it is two standard deviations below the mean.

The z-score of any number x in a normal distribution is given by

where x is the score, is the mean and is the standard deviation.