Calculate Standard Deviation

My textarea:

Text format:

Your current progress:

Number 1: *

Number 2: *

Number 3: *

Number 4: *

Number 5: *

Formula

#sum = [num1] + [num2] + [num3] + [num4] + [num5]

#n = 5

#average = #sum / #n

#x1 = [num1] - #average

#x2 = [num2] - #average

#x3 = [num3] - #average

#x4 = [num4] - #average

#x5 = [num5] - #average

#xx1 = #x1 * #x1

#xx2 = #x2 * #x2

#xx3 = #x3 * #x3

#xx4 = #x4 * #x4

#xx5 = #x5 * #x5

#sum = #xx1 + #xx2 + #xx3 + #xx4 + #xx5

#sumroot = #sum / #n

#root = sqrt([#sumroot])

#power = pow(2,3)

Step 1 - Write the formula

σ = √ ( ∑ ( x - mean )² / N )

Step 2 - How many numbers are there? (N)

In this example, there are [#n] numbers in the array.

So,

N = [#n]

Which means:

σ = √ ( ∑ ( x - mean )² / [#n] )

Step 3 - Calculate the mean

Mean = ( [num1] + [num2] + [num3] + [num4] + [num5] ) / [#n] = [#average]

σ = √ ( ∑ ( x - [#average] )² / [#n] )

Step 4 - What are the respective deviations from the mean?

Here, we calculate how much each value is from the mean value

x₁ = [num1] - [#average] = [#x1]
x₂ = [num2] - [#average] = [#x2]
x₃ = [num3] - [#average] = [#x3]
x₄ = [num4] - [#average] = [#x4]
x₅ = [num5] - [#average] = [#x5]

Which means:

σ = √ ( ∑ ( x - [#average] )² / [#n] ) = √ ( ∑ ( x₁² + x₂² + x₃² + x₄² + x₅² ) / [#n] )

σ = √ ( ( [#x1]² + [#x2]² + [#x3]² + [#x4]² + [#x5]² ) / [#n] )

Step 5 - Calculate squares

σ = √ ( ( [#xx1] + [#xx2] + [#xx3] + [#xx4] + [#xx5] ) / [#n] )

Step 6 - Sum it together

σ = [#sumroot]

Step 7 - Square root the total:

σ = [#root]

So that is the answer. The standard deviation of [num1], [num2], [num3], [num4] and [num5] is [#root].

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