- Trending Categories
- Data Structure
- Operating System
- C Programming
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Let’s first get to know about mean, variance and standard deviation
Consider the following array of numbers −
arr: [10, 20, 30, 40]
And let’s calculate the mean, variance, and standard deviation of this array.
Mean − It is the average of all the array elements.
In a simple way it is sum of all the array element / number of array element.
mean= (10+20+30+40)/4 = 25
Variance − The variance is the sum of the squared difference from the mean / number of array element.
Variance= ((10-25)^2 +(20-25)^2 +(30-25)^2 +(40-25)^2 ) / 4 = ( 225 + 100 + 25 + 225 ) / 4 = 143.75
Standard Deviation − It is square root of the variance.
Standard deviation = (variance)^1/2 Standard Deviation= (143.75)^1/2= 11.989
Basically, standard deviation is calculation of how far a collection of number deviate from the average. When standard deviation is there it means numbers are close to the mean.
Step 1 − Calculate mean of the given array first
Step 2 − Calculate variance of that array using mean
Step 3 − Finally Calculate Standard Deviation by help of calculated mean and variance.
Step 1: Calculate mean of the given array first
arr: [1, 2, 3, 4, 5]
and we will perform all the calculation on this array.
As we have to calculate mean so we will have to get the sum of the array so we use here Array.reduce() method as you know reduce method reduce the array to the single value, so single which will be sum it will return then we will divide that sum with number of array elements.
const mean=arr.reduce((ele1, ele2) => ele1+ele2) / 5 //here 5 is the array size //mean = 15/5 = 3
Step 2: Calculate variance of that array using mean
For calculating variance, we will use map method and while traversing we will calculate (current element-mean)^2 to all the array items.
const variance= arr.map(ele=> Math.pow(ele- mean, 2)).reduce((a, b) =>a+b) //variance= (4+1+0+1+4) / 5 = 2
Step 3: Finally Calculate Standard Deviation
For Standard Deviation, simply apply Math.sqrt (variance).
const standard_dev= Math.sqrt(variance) //(2)^1/2= 1.4142135623730951
Here when the button Calculate will be clicked then it will call the function Standard_deviation which will calculate the standard deviation of the provided array, you can check by changing the values of the array.
So, this is how we saw the procedure to find the standard deviation of an array of numbers.
- PHP program to find standard deviation of values within an array
- Print the standard deviation of Pandas series
- Return the standard deviation of the masked array elements in NumPy
- What is Standard Deviation of Return?
- How to find the moving standard deviation in an R matrix?
- Average Returns and Standard Deviation of Securities
- Return the standard deviation of the masked array elements along given axis in NumPy
- Return the standard deviation of the masked array elements along row axis in NumPy
- Return the standard deviation of the masked array elements along column axis in NumPy
- C++ program to implement standard deviation of grouped data
- How to find the moving standard deviation in an R data frame?
- C program to calculate the standard deviation
- Variance and Standard Deviation
- Calculating the standard deviation of all pixels for each band in an image using the Pillow library
- How to compute the mean and standard deviation of a tensor in PyTorch?