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Q39E

Expert-verifiedFound in: Page 136

Book edition
2nd Edition

Author(s)
Randy Harris

Pages
633 pages

ISBN
9780805303087

**Verify the claim made in a section 4.4** **that if all results of a repeated experiment are equal, the standard deviation, equation (4.13)** **Will be** **0****.**

The standard deviation is 0.

For a given set of results, the standard deviation is the same and equal to 0.

**We can solve for both quantities by directly applying the mean and standard deviation definitions given by equations (1) and (2) respectively. Here, refers to the outcome of each measurement, and refers to the number of these measurements.**

**$\overline{)\mathbf{Q}}{\mathbf{=}}\frac{\mathbf{\sum}_{\mathbf{i}}{\mathbf{Q}}_{\mathbf{i}}{\mathbf{n}}_{\mathbf{i}}}{\mathbf{\sum}_{\mathbf{i}}{\mathbf{n}}_{\mathbf{i}}}$ ………………(1)**

** **

**role="math" localid="1658322728674" ${\mathbf{\u2206}}{\mathit{Q}}{\mathbf{=}}\sqrt{\frac{\mathbf{\sum}_{\mathbf{i}}{\mathbf{(}{\mathbf{Q}}_{\mathbf{i}}\mathbf{-}{\overline{)\mathbf{Q}}}_{\mathbf{i}}\mathbf{)}}^{\mathbf{2}}{\mathbf{n}}_{\mathbf{i}}}{\mathbf{\sum}_{\mathbf{i}}{\mathbf{n}}_{\mathbf{i}}}}$ ****……………………(2)**

When Q is a constant and can be removed from the equation, the expression is calculated as,

$\begin{array}{rcl}\u2206Q& =& {\left[\frac{\sum _{i}{({Q}_{i}-\overline{){Q}_{i}})}^{2}{n}_{i}}{\sum _{i}{n}_{i}}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\\ & =& 0\end{array}$

As a result, the standard deviation for a particular set of outcomes is equal 0.

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