{"id":4636,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-15-2\/"},"modified":"2016-05-17T13:38:31","modified_gmt":"2016-05-17T08:08:31","slug":"ncert-solutions-class-11-maths-exercise-15-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-15-2\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 15.2"},"content":{"rendered":"

Exercise 15.2<\/strong><\/p>\n

Find the mean and variance for each of the data in Exercises 1 to 5.<\/strong><\/p>\n

1. 6, 7, 10, 12, 13, 4, 8, 12<\/strong><\/p>\n

Ans. <\/strong>Given: = 6, 7, 10, 12, 13, 4, 8, 12<\/p>\n

= 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72<\/p>\n

And = 8 = 9<\/p>\n

Also = 722<\/p>\n

Variance = <\/p>\n

= <\/p>\n

= = 9.25<\/p>\n

\n

2. First <\/strong> natural numbers<\/strong><\/p>\n

Ans. <\/strong>Given: 1, 2, 3, 4, \u2026\u2026\u2026\u2026., <\/p>\n

<\/p>\n

And <\/p>\n

Mean <\/p>\n

Now, Variance = <\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

= <\/p>\n

\n

3. First 10 multiples of 3<\/strong><\/p>\n

Ans. <\/strong>Given: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30<\/p>\n

<\/p>\n

And <\/p>\n

Mean <\/p>\n

Now, Variance = <\/p>\n

= <\/p>\n

= <\/p>\n

= = 74.25<\/p>\n

\n

4. <\/strong><\/p>\n

<\/p>\n

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

<\/p>\n

Mean = = 19<\/p>\n

Variance = <\/p>\n

= = 43.4<\/p>\n

\n

5. <\/strong><\/p>\n

<\/p>\n

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

<\/p>\n

Mean = = 22<\/p>\n

Variance = <\/p>\n

= = 29.09<\/p>\n

\n

6. Find the mean and standard deviation using short cut method.<\/strong><\/p>\n

<\/p>\n

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

<\/p>\n

Mean = = 64<\/p>\n

Variance = <\/p>\n

= <\/p>\n

= = = 1.69<\/p>\n

\n

Find the mean and variance for the following frequency distribution in Exercises 7 and 8.<\/strong><\/p>\n

7. <\/strong><\/p>\n

<\/p>\n

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

<\/p>\n

Mean = = 107<\/p>\n

Variance = = = 2280 \u2013 4 = 2276<\/p>\n

\n

8. <\/strong><\/p>\n

<\/p>\n

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

<\/p>\n

Mean <\/p>\n

= = 25 + 2 = 27<\/p>\n

Variance = <\/p>\n

= <\/p>\n

= = 132<\/p>\n

\n

9. Find the mean, variance and standard deviation using short-cut method.<\/strong><\/p>\n

<\/p>\n

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

<\/p>\n

Mean <\/p>\n

= = 92.5 + 0.5 = 93<\/p>\n

Variance = <\/p>\n

= <\/p>\n

= <\/p>\n

= = 105.58<\/p>\n

Standard deviation = 10.27<\/p>\n

\n

10. The diameters of circles (in mm) drawn in a design are given below:<\/strong><\/p>\n

<\/p>\n

Calculate the standard deviation and mean diameter of the circles.<\/strong><\/p>\n

[Hint: First make the data continuous by making the classes as 32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5-48.5, 48.5-52.5 and the proceed]<\/strong><\/p>\n

Ans.<\/p>\n

<\/p>\n

Mean <\/p>\n

= = 42.5 + 1 = 43.5 mm<\/p>\n

Standard deviation <\/p>\n

= <\/p>\n

= = 5.55<\/p>\n","protected":false},"excerpt":{"rendered":"

Exercise 15.2 Find the mean and variance for each of the data in Exercises 1 to 5. 1. 6, 7, 10, 12, 13, 4, 8, 12 Ans. Given: = 6, 7, 10, 12, 13, 4, 8, 12 = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72 … 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-4636","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"\nNCERT Solutions class-11 Maths Exercise 15.2 | 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-exercise-15-2\/\" \/>\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 Exercise 15.2 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 15.2 Find the mean and variance for each of the data in Exercises 1 to 5. 1. 6, 7, 10, 12, 13, 4, 8, 12 Ans. Given: = 6, 7, 10, 12, 13, 4, 8, 12 = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72 ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-15-2\/\" \/>\n<meta property=\"og:site_name\" content=\"myCBSEguide\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/mycbseguide\/\" \/>\n<meta property=\"article:published_time\" content=\"2016-05-17T06:19:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2016-05-17T08:08:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch15\/Ex15.2\/image001.png\" \/>\n<meta name=\"author\" content=\"myCBSEguide\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:site\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"myCBSEguide\" \/>\n\t<meta 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