{"id":12644,"date":"2022-12-20T23:52:47","date_gmt":"2022-12-20T18:22:47","guid":{"rendered":"https:\/\/mathemerize.com\/?p=12644"},"modified":"2022-12-20T23:52:51","modified_gmt":"2022-12-20T18:22:51","slug":"the-following-table-gives-the-distribution-of-the-life-time-of-400-neon-lamps-find-the-median-life-time-of-a-lamp","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-following-table-gives-the-distribution-of-the-life-time-of-400-neon-lamps-find-the-median-life-time-of-a-lamp\/","title":{"rendered":"The following table gives the distribution of the life time of 400 neon lamps. Find the median life time of a lamp."},"content":{"rendered":"\n

Question :<\/h2>\n\n\n\n
Life time (in hours)<\/td>Number of lamps<\/td><\/tr>
1500 – 2000<\/td>14<\/td><\/tr>
2000 – 2500<\/td>56<\/td><\/tr>
2500 – 3000<\/td>60<\/td><\/tr>
3000 – 3500<\/td>86<\/td><\/tr>
3500 – 4000<\/td>74<\/td><\/tr>
4000 – 4500<\/td>62<\/td><\/tr>
4500 – 5000<\/td>48<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

First, we prepare the following table to compute the median :<\/p>\n\n\n\n

Life time (in hours)<\/td>Number of lamps<\/td>Cumulative frequency<\/td><\/tr>
1500 – 2000<\/td>14<\/td>14<\/td><\/tr>
2000 – 2500<\/td>56<\/td>70<\/td><\/tr>
2500 – 3000<\/td>60<\/td>130<\/td><\/tr>
3000 – 3500<\/td>86<\/td>216<\/td><\/tr>
3500 – 4000<\/td>74<\/td>290<\/td><\/tr>
4000 – 4500<\/td>62<\/td>352<\/td><\/tr>
4500 – 5000<\/td>48<\/td>400<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

We have : n = 400 So, \\(n\\over 2\\) = 200<\/p>\n\n\n\n

The cumulative frequency just greater than \\(n\\over 2\\) is 216 and the corresponding class is (3000 – 3500). Thus, it is the median class.<\/p>\n\n\n\n

Here, l = 3000, cf = 130, f = 86 and h = 500.<\/p>\n\n\n\n

Substituting these values in the formula,<\/p>\n\n\n\n

Median = l + (\\({n\\over 2} – cf\\over f\\))\\(\\times\\)h, we have :<\/p>\n\n\n\n

Median = 3000 + \\(70\\over 86\\) \\(\\times\\) 500 = 3000 + 406.98 = 3406.98<\/p>\n\n\n\n

Hence, median life time is 3406.98 hours<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Life time (in hours) Number of lamps 1500 – 2000 14 2000 – 2500 56 2500 – 3000 60 3000 – 3500 86 3500 – 4000 74 4000 – 4500 62 4500 – 5000 48 Solution : First, we prepare the following table to compute the median : Life time (in hours) Number …<\/p>\n

The following table gives the distribution of the life time of 400 neon lamps. Find the median life time of a lamp.<\/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 table gives the distribution of the life time of 400 neon lamps. 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