Standard Deviation Calculator

Steps for Calculation

1. Input Numbers:
   • Enter a set of numbers separated by commas (e.g., 5, 10, 15, 20) in the input field.
2. Calculate:
   • Click the Calculate button to compute the standard deviation.
3. View Result:
   • The standard deviation of the numbers will be displayed below the button.

---

Detailed Description

• Standard Deviation:
  • Standard deviation is a measure of the amount of variation or dispersion in a set of values.
  • A low standard deviation indicates that the values are close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
• Steps to Calculate Standard Deviation:
  1. Calculate the Mean:
     • The mean (average) is calculated by summing all the numbers and dividing by the count of numbers.
     • Formula: Mean=∑i=1nxinMean=n∑i=1n​xi​​.
  2. Calculate the Variance:
     • The variance is the average of the squared differences from the mean.
     • Formula: Variance=∑i=1n(xi−Mean)2nVariance=n∑i=1n​(xi​−Mean)2​.
  3. Calculate the Standard Deviation:
     • The standard deviation is the square root of the variance.
     • Formula: Standard Deviation=VarianceStandard Deviation=Variance​.
• Example:
  • For the numbers 5, 10, 15, 20:
    • Mean = (5+10+15+20)/4=12.5(5+10+15+20)/4=12.5.
    • Variance = [(5−12.5)2+(10−12.5)2+(15−12.5)2+(20−12.5)2]/4=31.25[(5−12.5)2+(10−12.5)2+(15−12.5)2+(20−12.5)2]/4=31.25.
    • Standard Deviation = 31.25≈5.590231.25​≈5.5902.