In this article, I will explain how to calculate z score in R using the z score formula. We will calculate the mean and standard deviation for the vector using the r function and later calculate the z score.
What is a Z-Score?
Z-score is the distance of raw score value from the mean in terms of standard deviation. Raw scores above the mean have a positive Z-score value, while a raw score below the mean has a negative z-score value.
Steps to Calculate Z-score in R
- Step-1: Create the vector for the given data
- Step-2: Calculate the mean of the vector using the mean() function.
- Step-3: Calculate the standard deviation of the vector using the sd() function.
- Step-4: Calculate the z-score using the formula.
data- mean(data)) / sd(data)
- Step-5: The resultant vector will give the required z-score values.
Cool Tip: Read more on how to calculate z score on TI-84 plus!
Let’s understand how to find a z-score using R for a given vector using the step-by-step guide.
Calculate Z-score in R for the given vector
Let’s consider an example where we have sample data points from a given data set to find a z score.
Prepare vector in r to find mean and standard deviation
First, create a vector for given data points and assign it to the data variable.
Use the mean function to calculate the mean for a given vector
Use standard deviation (sd) function to calculate the standard deviation for a given vector
To calculate the z score in r put the calculated mean and standard deviation in the z score formula, it will find the z-score, and assign it to the zscore variable.
Use below R code to calculate z-score.
Z-Score in R code
# create the vector for given data data <- c(19, 11, 12, 14, 15, 18, 19) # Calculate mean mean(data) # Calculate standard deviation sd(data) # calculate z-score zscore <- (data - mean(data)) / sd(data) zscore
#Results mean(data)  15.42857 > > sd(data)  3.309438 > zscore  1.0791646 -1.3381641 -1.0359980 -0.4316658  -0.1294998 0.7769985 1.0791646
Interpretation of z-scores
- The z-score for data value 19 is 1.0791646. It means it is 1.0791646 standard deviation above the mean.
- The z-score for data value 11 is -1.3381641. It means it is -1.3381641 standard deviation below the mean.
- The z-score for data value 12 is -1.0359980. It means it is -1.0359980 standard deviation below the mean.
- The z-score for data value 14 is -0.4316658. It means it is -0.4316658 standard deviation below the mean.
Similarly, we can interpret the other z-scores.
Cool Tip: Read more on how to Calculate Z Score in Excel!
Plot the Calculated Z-score for given vector in R
# create the vector for given data data <- c(19, 11, 12, 14, 15, 18, 19) # Calculate mean mean(data) # Calculate standard deviation sd(data) # calculate z-score zscore <- (data - mean(data)) / sd(data) zscore # plot z-score plot(zscore, type="o", col="green")
The resultant plot for the calculated z score for the given data set is shown below.
I hope the above article helps you to calculate the z score using r. We have learned how to prepare a vector for a given dataset and find the mean and standard deviation.
Using the z-score formula, we can find the z-score in r and plot the z-score on a chart.
You can read more about
How to find an area to the left for the given z
Find the area between the two z-scores.
Find the z-score for having area 0.09