{"id":7008,"date":"2021-10-22T14:43:51","date_gmt":"2021-10-22T09:13:51","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7008"},"modified":"2021-10-25T09:18:39","modified_gmt":"2021-10-25T03:48:39","slug":"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","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/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\/","title":{"rendered":"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"},"content":{"rendered":"

Solution :<\/h2>\n

In the 2n observations, half of them equals a and remaining half equal -a. Then, the mean of total 2n observations is equal to 0.<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0SD = \\(\\sqrt{\\sum(x – \\bar{x})^2\\over N}\\)<\/p>\n

\\(\\implies\\)\u00a0 4 = \\(\\sum{x^2}\\over 2n\\)<\/p>\n

\\(\\implies\\)\u00a0 4 = \\(2na^2\\over 2n\\)<\/p>\n

\\(\\implies\\)\u00a0 \\(a^2\\) = 4<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0a = 2<\/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

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is<\/a><\/p>\n

A random variable X has poisson distribution with mean 2. Then, P(X > 1.5) equal to<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : In the 2n observations, half of them equals a and remaining half equal -a. Then, the mean of total 2n observations is equal to 0. \\(\\therefore\\)\u00a0 \u00a0SD = \\(\\sqrt{\\sum(x – \\bar{x})^2\\over N}\\) \\(\\implies\\)\u00a0 4 = \\(\\sum{x^2}\\over 2n\\) \\(\\implies\\)\u00a0 4 = \\(2na^2\\over 2n\\) \\(\\implies\\)\u00a0 \\(a^2\\) = 4 \\(\\therefore\\)\u00a0 \u00a0a = 2 Similar Questions The …<\/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<\/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":"\nIn a series of 2n observations, half of them equals a and remaining half equal -a. 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(therefore)\u00a0 \u00a0SD = (sqrt{sum(x – bar{x})^2over N}) (implies)\u00a0 4 = (sum{x^2}over 2n) (implies)\u00a0 4 = (2na^2over 2n) (implies)\u00a0 (a^2) = 4 (therefore)\u00a0 \u00a0a = 2 Similar Questions The … In a series of 2n observations, half of them equals a and remaining half equal -a. 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