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Statistics

Long Answer Type

491. The diameters of circles (in mm) drawn in a design are given below:

Calculate the standard deviation and mean diameter of the circles.

First of all, we shall make class-intervals continuous:

(a) Mean = $straight A space plus fraction numerator sum f u over denominator straight N end fraction cross times i space equals space 42.5 space plus space 25 over 100 cross times 4 space equals space 43.5$

(b) S.D. = $space space space fraction numerator square root of straight N begin display style sum from blank to blank of end style f u squared minus left parenthesis begin display style sum from blank to blank of end style f u right parenthesis squared end root over denominator straight N end fraction space equals space fraction numerator square root of 100 left parenthesis 199 right parenthesis minus left parenthesis 25 right parenthesis squared end root over denominator 100 end fraction cross times 4 space equals space fraction numerator square root of 19275 over denominator 25 end fraction equals fraction numerator square root of 771 over denominator 5 end fraction equals 5.55$

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492. The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and S.D. in each of the following cases: (i) If the wrong item is omitted (ii) If it is replaced by 12.

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Short Answer Type

493.

If the observations x₁, x₂,........ x_n are changed to x₁ + a, x₂ + a, x₃ + a, x_n+ a, where a is a negative or positive number, show that the variance remains unchanged.

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Long Answer Type

494. The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6. Find the other two observations.

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495.

Given that $top enclose straight x$ is the mean and $straight sigma squared$ is the variance of n observations $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ Prove that the mean and variance of observations $ax subscript 1 comma space ax subscript 2 comma space ax subscript 3 comma space....... comma space ax subscript straight n$ are $straight a space top enclose straight x space and space straight a squared space straight sigma squared$ respectively, $left parenthesis straight a not equal to 0 right parenthesis.$

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496. The mean and standard deviation of a group of 100 observations was found to be 20 and 3 respectively. Later on it was found that three observations were incorrect, which were recorded as 21,21 and 18. Find the standard deviation, if the incorrect observations were omitted.

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