The formula to calculate the Z score is:
\[ Z = \frac{R - \mu}{\sigma} \]
where \( Z \) is the Z score, \( R \) is the raw score, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
A Z score, also known as a standard score, is a statistical measurement that describes a value’s relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. A Z score of 0 indicates that the data point’s score is identical to the mean score. Z scores may be positive or negative, with a positive value indicating the score is above the mean and a negative value indicating it is below the mean. Z scores are commonly used in statistics to understand the distribution of data and to identify outliers.
Let's assume we have the following values:
Step 1: Subtract the mean from the raw score:
\[ R - \mu = 85 - 75 = 10 \]
Step 2: Divide the result by the standard deviation:
\[ Z = \frac{10}{5} = 2 \]
Therefore, the Z score is \( Z = 2 \).
