{"id":4638,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-13\/"},"modified":"2016-05-17T13:40:04","modified_gmt":"2016-05-17T08:10:04","slug":"ncert-solutions-class-11-maths-miscellaneous-13","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-13\/","title":{"rendered":"NCERT Solutions class-11 Maths Miscellaneous"},"content":{"rendered":"

Miscellaneous Exercise <\/strong><\/p>\n

1. The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.<\/strong><\/p>\n

Ans. <\/strong>Let two required observations be and Then,<\/p>\n

According to question, <\/p>\n

<\/p>\n

\u2026\u2026\u2026.(i)<\/p>\n

Also <\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(ii)<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

When then on solving and we get and <\/p>\n

When then on solving and we get and <\/p>\n

\n

2. The mean and variance of 7 observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12, 14, find the remaining two observations.<\/strong><\/p>\n

Ans. <\/strong>Let two required observations be and Then,<\/p>\n

According to question, <\/p>\n

<\/p>\n

\u2026\u2026\u2026.(i)<\/p>\n

Also <\/p>\n

<\/p>\n

<\/p>\n

\u2026\u2026\u2026.(ii)<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

When then on solving and we get and <\/p>\n

When then on solving and we get and <\/p>\n

\n

3. The mean and standard deviation of six observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.<\/strong><\/p>\n

Ans. <\/strong>Let six observations be then<\/p>\n

According to questions, <\/p>\n

<\/p>\n

Now, if each observation is multiplied by 3, then<\/p>\n

New mean = = 24<\/p>\n

Also <\/p>\n

<\/p>\n

Now, if each observation is multiplied by 3, then<\/p>\n

New Variance = <\/p>\n

= 720 \u2013 576 = 144<\/p>\n

Therefore, New S.D. = = 12<\/p>\n

\n

4. Given that <\/strong> is the mean and <\/strong> is the variance of <\/strong> observations <\/strong> Prove that the mean and variance of the observations <\/strong> are <\/strong> and <\/strong> respectively <\/strong><\/p>\n

Ans. <\/strong>Given: <\/p>\n

Also <\/p>\n

New Mean =<\/p>\n

Also <\/p>\n

New Variance = <\/p>\n

= <\/p>\n

= <\/p>\n

\n

5. 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 standard deviation in each of the following cases:<\/strong><\/p>\n

(i) if wrong item is omitted <\/strong><\/p>\n

(ii) if it is replaced by 12.<\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

Now, <\/p>\n

<\/p>\n

<\/p>\n

Incorrect <\/p>\n

Now <\/p>\n

<\/p>\n

<\/p>\n

(i)<\/strong> If wrong item is omitted: then we have 19 observations.<\/p>\n

Correct = Incorrect <\/p>\n

Correct = 200 \u2013 8 = 192<\/p>\n

Correct Mean = = 10.1<\/p>\n

Also Correct Incorrect <\/p>\n

Correct Variance = (Correct ) \u2013 (Correct mean)2<\/sup><\/p>\n

= = = <\/p>\n

Correct S.D. = = 1.997<\/p>\n

(ii)<\/strong> If it is replaced by 12: then<\/p>\n

Correct = Incorrect <\/p>\n

Correct = 200 \u2013 8 + 12 = 204<\/p>\n

Correct Mean = = 10.2<\/p>\n

Also Correct Incorrect<\/p>\n

<\/p>\n

Correct Variance = (Correct ) <\/p>\n

= = = <\/p>\n

Correct S.D. = = 11.989<\/p>\n

\n

6. The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:<\/strong><\/p>\n

<\/p>\n

Which of the three subjects shows the highest variability in marks and which shows the lowest?<\/strong><\/p>\n

Ans. <\/strong>For Mathematics, = 42 and = 12<\/p>\n

C.V. of Mathematics = = 28.57%<\/p>\n

For Physics, = 32 and = 15<\/p>\n

C.V. of Physics = = 46.88%<\/p>\n

For Chemistry, = 40.9 and = 20<\/p>\n

C.V. of Chemistry = = 48.9%<\/p>\n

Therefore, Chemistry with highest C.V. shows highest variability and Mathematics with lowest C.V. shows lowest variability.<\/p>\n

\n

7. The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect, which were recorded as 12, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.<\/strong><\/p>\n

Ans. <\/strong>Given: and <\/p>\n

Now, <\/p>\n

<\/p>\n

<\/p>\n

Incorrect <\/p>\n

Now <\/p>\n

<\/p>\n

<\/p>\n

When wrong items 21, 21 and 18 are omitted from the data, then there will be 97 observations.<\/p>\n

Correct = Incorrect <\/p>\n

Correct = 2000 \u2013 21 \u2013 21 \u2013 18 = 1940<\/p>\n

Correct Mean = = 20<\/p>\n

Also Correct Incorrect <\/p>\n

<\/p>\n

Correct Variance = (Correct ) \u2013 (Correct mean)2<\/sup><\/p>\n

= = = <\/p>\n

Correct S.D. = = 3.036<\/p>\n","protected":false},"excerpt":{"rendered":"

Miscellaneous Exercise 1. The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations. Ans. Let two required observations be and Then, According to question, \u2026\u2026\u2026.(i) Also \u2026\u2026\u2026.(ii) When then on solving and we get and … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4638","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Miscellaneous | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-miscellaneous-13\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Miscellaneous | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Miscellaneous Exercise 1. The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations. Ans. Let two required observations be and Then, According to question, \u2026\u2026\u2026.(i) Also \u2026\u2026\u2026.(ii) When then on solving and we get and ... 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