Finding The Standard Deviation Of Numbers

Finding the standard deviation of numbers is as simple as the square root of the variance in statistics.

In this lesson, you will learn the formula and the step-by-step method for finding the standard deviation of numbers.

BONUS: A link to practice questions on statistics is included at the end of this lesson.

Formula for finding the standard deviation of numbers

The formula for finding the standard deviation of numbers is the square root of the variance.

SD=\sqrt{V}

Where:

  • SD = Standard Deviation
  • V = Variance

Question on finding the standard deviation of numbers

Question

Find the standard deviation of the following numbers:

15, 11, 8, 3, 13 , 8, 5

STEP 1.

Find the variance of the numbers

Working

The variance of 15, 11, 8, 3, 13 , 8, 5

= 15.71

STEP 2.

Find the square root of the variance

\sqrt{15.71} = 3.96

Final answer

The standard deviation of the following numbers:

15, 11, 8, 3, 13 , 8, 5

= 3.96

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