Z Score Calculator
Z Score calculator calculates the standard score for any raw score. Z Score is a measure that is used to describe the relationship between a raw score and the mean value of the given data set. Z scores are also called standard scores.
What is Z Score Calculator?
Z Score Calculator is an online tool used to calculate the z score for the given mean, raw score, and standard deviation. The z score tells us the number of standard deviations by which the raw score is above or below the mean of the data. To use this z score calculator, enter values in the input boxes.
Z Score Calculator
NOTE: Enter values upto 5 digits only
How to Use Z Score Calculator?
Use the steps given below to find the z score using the online z score calculator:
- Step 1: Go to Cuemath’s online z score calculator.
- Step 2: Enter the values of the raw score, the mean, and the standard deviation in the input boxes of the z score calculator.
- Step 3: Click on the "Calculate" button to find the z score.
- Step 4: Click on the "Reset" button to clear the fields and enter new values.
How Does Z Score Calculator Work?
Z score can be both positive and negative. A positive z score indicates that the raw score is above the mean. Similarly, a negative z score denotes that the raw score is below the mean. Furthermore, if we have a z score that is equal to 1, it implies that the raw score is 1 standard deviation above the mean. If the z score is -2, it shows that the raw score is 2 standard deviations below the mean of the given data. The steps to calculate the z score are as follows:
- Subtract the mean of the population from the given raw score. The mean is given by \(\mu\) while x denotes the raw score.
- Divide the value obtained in step 1 by the standard deviation to get the z score. The standard deviation is represented by \(\sigma\).
The formula for calculating the z score is given as follows:
Z score = \(\frac{x - \mu }{\sigma }\).
The calculator replaces \(\mu\) with u and \(\sigma\) by v.
Solved Examples on Z Score Calculator
Example 1:
Find the Z-score for a raw score of 5, mean 3, and standard deviation 1 and verify it using the z score calculator.
Solution:
Given raw score x = 5, mean \(\mu\) = 3 and standard deviation \(\sigma\) = 1
z = \(\frac{x - \mu }{\sigma }\) = (5 - 3)/1 = 2
z score is positive indicating that the raw score is above the mean.
Example 2:
Find the Z-score for a raw score of 8, mean 10, and standard deviation 2 and verify it using the z score calculator.
Solution:
Given raw score x = 8, mean \(\mu\) = 10 and standard deviation \(\sigma\) = 1
z = \(\frac{x - \mu }{\sigma }\) = (8 - 10)/2 = -1
z value is negative indicating that the raw score is below the mean.
Similarly, you can try the Z-score calculator to find the Z-score for the following:
- Find Z-score when raw score = 5, mean = 10 , standard deviation = 2
- Find Z-score when raw score = 20, mean = 15 , standard deviation = 5