All Calculator.net's As an academician, analyst, or researcher, one can avoid taking the pain of calculating using pen and paper; instead, this Z-score calculator comes in handy for your quick calculation without a mess and the use of excel.
For Example: The result of a particular college entrance exam has a mean score of 80 and a standard deviation of 5.
If students received 88 scores on an exam, then the Z-score can be calculated based on the formula as
z = (x – μ) / σ
z = (88 – 80) / 5
z = 1.6
This indicates that the student's score was 1.6 standard deviations outside the mean.
We might determine that a z-score of 1.6 signifies a value greater than 94.52% of all exam results using the Area to the Left of the Z-Score Calculator.
- A value is equal to the mean if its z-score equals zero.
- A value is 1.3 standard deviations below the mean if it has a z-score of -1.3.
- A value is 2.2 standard deviations above the mean if its z-score equals 2.2.
Other real-time examples are
- one can find the Z-Score value of newborn baby weight while comparing it with the mean population of all newborn babies' weight and standard deviation.
- Z-scores are frequently used in biology to compare an individual animal's height to the average height of its group.
- Z-scores can be used to compare a particular shoe size to the average population.
- Z-scores are frequently used in medical contexts to compare a person's blood pressure to the average blood pressure of the population.
- A z-score can be converted to a percentile to assist you in figuring out what proportion of values in a distribution the value falls within.
- After finding the Z-score, one must find the value associated with the score using the Z table.
A z-table provides the area under the curve to the left of a z-score, also referred to as the standard normal table. This region denotes the likelihood that a given region of the standard normal distribution will contain z-values.
A z-score table displays the percentage of values (often expressed as a decimal number) on a normal distribution to the left of a specific z-score. Consider that our Z-score is 1.09 as an illustration. Find the value that corresponds to one decimal place of the z-score by first looking at the left side column of the z-table (e.g., the whole number and the first digit after the decimal point). It is 1.0 in this instance. We then look up the last number, which in our Example is 0.09, across the table (on top).
In other words, 86.21% of the standard normal distribution lies below (or to the left) of the z-score, as indicated by the corresponding area of 0.8621.
This simple Z–score calculator does all the work, from computing to finding the exact value corresponding to the Z table.