Z-Scores & Z-tables

A Z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula: $$z = \frac{{X - \mu}}{{\sigma}}$$ where X is the value, \mu is the mean, and \sigma is the standard deviation.

A Z-score of 0 indicates that the data point is exactly at the mean of the data set.

A positive Z-score indicates that the data point is above the mean.

A negative Z-score indicates that the data point is below the mean.

A Z-table shows the percentage of values to the left of a given Z-score in a standard normal distribution.

In a standard normal distribution, the mean is 0.

In a standard normal distribution, the standard deviation is 1.

$$z = \frac{{70 - 52}}{{6}} = 3$$ .

$$z = \frac{{23 - 20}}{{3}} = 1$$ .

2.5% of students scored higher than the student.