The step-by-step z-score calculator calculates a z-score based on the z-score formula. First, enter values for the mean, standard deviation, and data value. The calculator will then give you an answer, and guide you through a solution so you can learn to solve this problem on your own.
Z-Score Calculator
Answer: -1.54
Solution:
Depending on what your distribution represents, start by either writing the formula for the z-score of a population: $$z = {{x-{\mu}} \over {\sigma}}$$
or the formula for the z-score of a sample: $$z = {{x-{\bar{x}}} \over s}$$
Substitute in values for this problem (data value, mean, and standard deviation) into the formula: $$z = {{128 - 148} \over 13}$$
If you are using a calculator, make sure you put the numerator in parentheses to ensure it is evaluated first. Here, we round the answer to 2 decimal places. $$z = \frac{(128 - 148)}{13}$$ $$z = -1.54$$