{"id":12324,"date":"2022-10-17T21:29:43","date_gmt":"2022-10-17T15:59:43","guid":{"rendered":"https:\/\/mathemerize.com\/?p=12324"},"modified":"2022-10-17T21:29:48","modified_gmt":"2022-10-17T15:59:48","slug":"the-following-data-gives-the-information-on-the-observed-lifetimes-in-hours-of-225-electrical-components-determine-the-modal-lifetime-of-the-components","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-following-data-gives-the-information-on-the-observed-lifetimes-in-hours-of-225-electrical-components-determine-the-modal-lifetime-of-the-components\/","title":{"rendered":"The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetime of the components"},"content":{"rendered":"\n

Question :<\/h2>\n\n\n\n
Lifetimes (in hours)<\/td>0 – 20<\/td>20 – 40<\/td>40 – 60<\/td>60 – 80<\/td>80 – 100<\/td>100 – 120<\/td><\/tr>
Frequency<\/td>10<\/td>35<\/td>52<\/td>61<\/td>38<\/td>29<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Solution :<\/h2>\n\n\n\n

The following (60 – 80) has the maximum frequency. Therefore, this is the modal class.<\/p>\n\n\n\n

Here, l = 60, h = 20, \\(f_1\\) = 61, \\(f_0\\) = 52 and \\(f_2\\) = 38<\/p>\n\n\n\n

Now, let us substitute these value in the formula<\/p>\n\n\n\n

Mode = l + (\\(f_1 – f_0\\over 2f_1 – f_0 – f_2\\))\\(\\times\\)h<\/p>\n\n\n\n

= 60 + (\\(61 – 52\\over 122 – 52 – 38\\))\\(\\times\\) 20<\/p>\n\n\n\n

= 60 + \\(9\\over 32\\) \\(\\times\\) 20<\/p>\n\n\n\n

= 60 + 5.625 = 65.625<\/p>\n\n\n\n

Thus, the modal lifetimes of the components is 65.625<\/strong> hours.<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Lifetimes (in hours) 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 Frequency 10 35 52 61 38 29 Solution : The following (60 – 80) has the maximum frequency. Therefore, this is the modal class. Here, l = 60, h = 20, \\(f_1\\) …<\/p>\n

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetime of the components<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","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":"","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 following data gives the information on the observed lifetimes (in hours) of 225 electrical components. 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