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Statistics

Long Answer Type

511. Find the mean and variance for the following frequency distribution:

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512. Find the mean and variance for the following distribution:

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513. Find the mean, variance and standard deviation using short-cut method.

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514. Calculate the mean, variance and standard deviation for the following distribution:

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515. Calculate the mean and S.D. for the following distribution:

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516. The following table gives the distribution of the income of 100 families in a village. Calculate the variance and standard deviation.

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517.

The runs scored by two batsmen in 10 innings are: A: 65, 58, 68, 44, 48, 45, 60, 62, 60, 50
B: 48, 80, 58, 44, 52.65, 73, 56, 64.50.
Which of the batsmen is more consistent and which one is more variable?

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518.

The marks obtained (out of 100) by two students in 10 qualifying tests were: A: 48, 53, 58, 41, 54, 52, 54, 49, 51, 50
B: 11, 98, 60, 94, 48, 52,17, 90, 20, 20
Who is more consistent in performance and who is more variable?

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519.

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Subject Mathematics Physics Chemistry
Mean 42 32 40.9

Standard
deviation 12 15 20
which of the three subjects shows the highest variability in marks and which shows the lowest?

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520.
An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:
Firm A Firm B
No. of wage earners 586 648
Mean of monthly wages Rs 5253 Rs 5253
Variance of the distribution of wages 100 121

(i) Which firm A or B pays larger amount as monthly wages?
(ii) Which firm A or B shows greater variability in individual wages?

Mean monthly wages for firm A, $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
No of workers, $straight n subscript 1 space equals space 586$
∴ $fraction numerator begin display style sum from blank to blank of end style straight X over denominator straight n subscript 1 end fraction equals top enclose straight X space space rightwards double arrow space space fraction numerator begin display style sum from blank to blank of end style straight X over denominator 586 end fraction space equals space 5253 space space rightwards double arrow space space sum from blank to blank of straight X space equals space Rs. space 5253 space cross times space 586 space equals space Rs. space 3078258$ ...(i)
Mean monthly wages for firm B,
$top enclose straight Y space equals space Rs. space 5253$
Number of workers, $straight n subscript 2 space equals space 648$

∴ $space space fraction numerator begin display style sum from blank to blank of straight Y end style over denominator straight n subscript 2 end fraction space equals space top enclose straight Y space rightwards double arrow space space fraction numerator begin display style sum from blank to blank of straight Y end style over denominator 648 end fraction space equals space 5253 space rightwards double arrow space sum from blank to blank of straight Y space equals space Rs. space 5253 space cross times space 648 space equals space Rs. space 3403944$
From (i) and (ii), we conclude that firm A pays Rs 30,78,258 p.m. to its workers whereas firm B pays Rs 34,03,944 p.m. Hence, firm B pays more.

(ii) The means of the two datas
$space space space top enclose straight X space equals space top enclose straight Y space equals space Rs space 5253$
∴ To compare the variability, we shall use only the standard deviations.
Variance for firm A, $straight sigma subscript 1 superscript 2 space equals space 100 space rightwards double arrow space space straight S. straight D. space left parenthesis straight sigma subscript 1 right parenthesis space equals space square root of 100 space equals space 10$
Variance for firm B, $space space space space space space space space straight sigma subscript 2 superscript 2 space equals space 121 space rightwards double arrow space straight S. straight D. space left parenthesis straight sigma subscript 2 right parenthesis space equals space square root of 121 space equals space 11$
$straight sigma subscript 2 greater than straight sigma subscript 1$
$rightwards double arrow$ Wages for firm B are more variable.

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