{"id":6962,"date":"2021-10-22T02:18:38","date_gmt":"2021-10-21T20:48:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6962"},"modified":"2021-10-25T09:32:38","modified_gmt":"2021-10-25T04:02:38","slug":"all-the-students-of-a-class-performed-poorly-in-mathematics-the-teacher-decided-to-give-grace-marks-of-10-to-each-of-the-students-which-statistical-measure-will-not-change-even-after-the-grace-marks","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/all-the-students-of-a-class-performed-poorly-in-mathematics-the-teacher-decided-to-give-grace-marks-of-10-to-each-of-the-students-which-statistical-measure-will-not-change-even-after-the-grace-marks\/","title":{"rendered":"All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ?"},"content":{"rendered":"

Question :<\/h2>\n

All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ?<\/p>\n

(a) Mean<\/p>\n

(b) Median<\/p>\n

(c) Mode<\/p>\n

(d) Variance<\/p>\n

Solution :<\/h2>\n

If initially all marks were given \\(x_i\\), then<\/p>\n

\\({\\sigma_i}^2\\) = \\(\\sum(x_i – \\bar{x})^2\\over N\\)<\/p>\n

Now, each is increased by 10.<\/p>\n

\\(\\therefore\\) \\({\\sigma_i}^2\\) = \\(\\sum((x_i + 10) – (\\bar{x} + 10))^2\\over N\\)<\/p>\n

= \\({\\sigma_i}^2\\)<\/p>\n

So, variance will not change whereas mean, median and mode will increase by 10.<\/p>\n

\n

Similar Questions<\/h3>\n

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The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new is<\/a><\/p>\n

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Question : All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ? (a) Mean (b) Median (c) Mode (d) Variance Solution : If initially all marks were …<\/p>\n

All the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. Which statistical measure will not change even after the grace marks were given ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,58],"tags":[],"yoast_head":"\nAll the students of a class performed poorly in mathematics. The teacher decided to give grace marks of 10 to each of the students. 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