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Statistics

Long Answer Type

481. The frequency distribution of population in males in different age groups is given below:
Calculate the mean deviation about the median.

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Short Answer Type

482. Find the mean and variance for the following data:
25, 50, 45, 30, 70, 42, 36, 48, 34, 50

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483. Find the mean and variance for the following data:
6, 7, 10, 12, 13, 4, 8, 12

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Long Answer Type

484. Find the mean and variance of the first n natural numbers.

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Short Answer Type

485. Find the variance and standard deviation of 3, 5, 5, 4, 6, 3, 5, 7,1, 8.

x = 3, 5, 5, 4, 6, 3, 5, 7,1, 8
$rightwards double arrow$ $sum straight x space equals space 47 comma space space straight N equals 10$
$rightwards double arrow$ $space space space space space top enclose straight x space equals space fraction numerator sum straight x over denominator straight N end fraction equals 47 over 10 equals 4.7$
which is not a whole number.
∴ We shall use formula, variance, $straight sigma squared space equals space fraction numerator straight N sum straight x squared minus left parenthesis sum straight x right parenthesis squared over denominator straight N squared end fraction$ ...(i)
$space space space sum straight x squared space equals space left parenthesis 3 right parenthesis squared plus left parenthesis 5 right parenthesis squared plus left parenthesis 5 right parenthesis squared plus left parenthesis 4 right parenthesis squared plus left parenthesis 6 right parenthesis squared plus left parenthesis 3 right parenthesis squared plus left parenthesis 5 right parenthesis squared plus left parenthesis 7 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 8 right parenthesis squared$
= 9 + 25 + 25 + 16 + 36 + 9 + 25 + 49 + 1 + 64 = 259
∴ Variance, $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
$straight S. straight D. space equals space square root of 3.81 end root space equals space 1.95$ .