Averages/Root mean square: Difference between revisions
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=={{header|AutoHotkey}}== |
=={{header|AutoHotkey}}== |
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'''Method 1 uses a loop to build the sum:''' |
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<lang autohotkey>MsgBox, % RMS(1, 10) |
<lang autohotkey>MsgBox, % RMS(1, 10) |
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Sum += (a + A_Index - 1) ** 2 |
Sum += (a + A_Index - 1) ** 2 |
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Return, Sqrt(Sum / n) |
Return, Sqrt(Sum / n) |
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}</lang> |
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Message box shows: |
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<pre> |
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6.204837 |
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</pre> |
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'''Method 2 does not need a loop:'''<br> |
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Using these equations:<br> |
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<math>\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}</math> See [[wp:List of mathematical series]]<br><br> |
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for <math>a<b</math> : <math>\sum_{i=a}^b i^2 = \sum_{i=1}^b i^2 - \sum_{i=1}^{a-1} i^2</math><br><br> |
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We can show that:<br> |
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<math>\sum_{i=a}^b i^2 = \frac{b(b+1)(2b+1)-a(a-1)(2a-1)}{6}</math> |
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<lang autohotkey>MsgBox, % RMS(1, 10) |
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;--------------------------------------------------------------------------- |
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RMS(a, b) { ; Root Mean Square of integers a through b |
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;--------------------------------------------------------------------------- |
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Return, Sqrt((b*(b+1)*(2*b+1)-a*(a-1)*(2*a-1))/6/(b-a+1)) |
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}</lang> |
}</lang> |
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Message box shows: |
Message box shows: |