{"id":6985,"date":"2021-10-22T14:24:14","date_gmt":"2021-10-22T08:54:14","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6985"},"modified":"2021-10-25T09:23:20","modified_gmt":"2021-10-25T03:53:20","slug":"the-mean-of-the-numbers-a-b-8-5-10-is-6-and-the-variance-is-6-80-then-find-the-values-of-a-and-b","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-mean-of-the-numbers-a-b-8-5-10-is-6-and-the-variance-is-6-80-then-find-the-values-of-a-and-b\/","title":{"rendered":"The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then, find the values of a and b?"},"content":{"rendered":"

Solution :<\/h2>\n

According to given condition,<\/p>\n

6.80 = \\((6-a)^2 + (6-b)^2 + (6-8)^2 + (6-5)^2 + (6-10)^2\\over 5\\)<\/p>\n

\\(\\implies\\)\u00a0 34 = \\((6-a)^2 + (6-b)^2\\) + 4 + 1 + 16<\/p>\n

\\(\\implies\\)\u00a0 \\((6-a)^2 + (6-b)^2\\) = 13<\/p>\n

\\(\\implies\\)\u00a0 \\((6-a)^2 + (6-b)^2\\) = 13 = \\(3^2\\) + \\(2^2\\)<\/p>\n

\\(\\implies\\)\u00a0 a = 3 and b = 4<\/p>\n

\n

Similar Questions<\/h3>\n

The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X = 1) is<\/a><\/p>\n

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

The mean and the variance of a binomial distribution are 4 and 2, respectively. Then, the probability of 2 success is<\/a><\/p>\n

In a series of 2n observations, half of them equals a and remaining half equal -a. If the standard deviation of the observation is 2, then |a| equal to<\/a><\/p>\n

The variance of first 50 even natural numbers is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : According to given condition, 6.80 = \\((6-a)^2 + (6-b)^2 + (6-8)^2 + (6-5)^2 + (6-10)^2\\over 5\\) \\(\\implies\\)\u00a0 34 = \\((6-a)^2 + (6-b)^2\\) + 4 + 1 + 16 \\(\\implies\\)\u00a0 \\((6-a)^2 + (6-b)^2\\) = 13 \\(\\implies\\)\u00a0 \\((6-a)^2 + (6-b)^2\\) = 13 = \\(3^2\\) + \\(2^2\\) \\(\\implies\\)\u00a0 a = 3 and b = 4 Similar …<\/p>\n

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then, find the values of a and b?<\/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":"\nThe mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. 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