Z-Score Calculator
Enter values below to calculate the Z-score.
Introduction to Z-Score
In statistics,aZ-score(or standard score)measures how many standard deviations a particular data point(or raw score)is away from the mean of a dataset.The formula for calculating the Z-score is:
Z=(X-μ)/σ
Where:
- X=Raw score(the data point)
- μ=Mean(average)of the dataset
- σ=Standard deviation(a measure of spread of the data)
The Z-score indicates how far and in what direction a data point deviates from the mean.It is particularly useful for identifying how unusual or significant a data point is within a given distribution.
Interpreting Z-Scores
A Z-score helps you understand where a particular value stands relative to the rest of the data:
- Z=0:The value is exactly at the mean.
- Z>0:The value is above the mean.
- Z<0:The value is below the mean.
- |Z|>2:The value is considered significantly different from the mean.
For example,if the mean test score in a class is70with a standard deviation of10,and a student scores80,the Z-score is:
Z=(80-70)/10=1.0
This means that the student's score is 1.0 standard deviation above the mean.
How to Use the Z-Score Calculator
Our Z-Score Calculator simplifies the process of calculating the Z-score.Follow these steps:
Step 1:Enter the Values
- Raw Score(X):The specific value you are analyzing.
- Mean(μ):The average value of your dataset.
- Standard Deviation(σ):The standard deviation of your dataset.
Step 2:Click the"Calculate Z-Score"Button
After entering the raw score,mean,and standard deviation,click the blueCalculate Z-Scorebutton to perform the calculation.
Step 3:View the Results
The result will appear below the button,showing the Z-score for the entered values.
Example Usage
If you enter:
- Raw Score(X)=85
- Mean(μ)=70
- Standard Deviation(σ)=10
Z=(85-70)/10=1.5
This means that the raw score of 85 is 1.5 standard deviations above the mean of 70.
Step 4:Interpret the Result
-A positive Z-score indicates that the value is above the mean.-A negative Z-score indicates that the value is below the mean.-A Z-score of 0 means the value is exactly at the mean.-If the Z-score is greater than 2 or less than-2,the value is significantly different from the mean.