{"id":12103,"date":"2022-09-15T23:49:24","date_gmt":"2022-09-15T18:19:24","guid":{"rendered":"https:\/\/mathemerize.com\/?p=12103"},"modified":"2022-09-15T23:49:27","modified_gmt":"2022-09-15T18:19:27","slug":"to-find-out-concentration-of-so_2-in-the-air-in-parts-per-million-i-e-ppm-the-data-was-collected-for-30-localities-in-a-certain-city-and-is-presented-below-find-the-mean-concentration-of","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/to-find-out-concentration-of-so_2-in-the-air-in-parts-per-million-i-e-ppm-the-data-was-collected-for-30-localities-in-a-certain-city-and-is-presented-below-find-the-mean-concentration-of\/","title":{"rendered":"To find out concentration of \\(SO_2\\) in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented below. Find the mean concentration of \\(SO_2\\) in the air."},"content":{"rendered":"\n

Question :<\/h2>\n\n\n\n
Concentration of \\(SO_2\\) (in ppm)<\/td>Frequency<\/td><\/tr>
0.00 – 0.04<\/td>4<\/td><\/tr>
0.04 – 0.08<\/td>9<\/td><\/tr>
0.08 – 0.12<\/td>9<\/td><\/tr>
0.12 – 0.16<\/td>2<\/td><\/tr>
0.16 – 0.20<\/td>4<\/td><\/tr>
0.20 – 0.24<\/td>2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

Let the assumed mean a = 0.10<\/p>\n\n\n\n

Concentration of \\(SO_2\\) (in ppm)<\/td>Frequency (\\(f_i\\))<\/td>Mid – Value (\\(x_i\\))<\/td>\\(u_i\\) = \\(x_i – 0.10\\over 0.04\\)<\/td>\\(f_iu_i\\)<\/td><\/tr>
0.00 – 0.04<\/td>4<\/td>0.02<\/td>-2<\/td>-8<\/td><\/tr>
0.04 – 0.08<\/td>9<\/td>0.06<\/td>-1<\/td>-9<\/td><\/tr>
0.08 – 0.12<\/td>9<\/td>0.10<\/td>0<\/td>0<\/td><\/tr>
0.12 – 0.16<\/td>2<\/td>0.14<\/td>1<\/td>2<\/td><\/tr>
0.16 – 0.20<\/td>4<\/td>0.18<\/td>2<\/td>8<\/td><\/tr>
0.20 – 0.24<\/td>2<\/td>0.22<\/td>3<\/td>6<\/td><\/tr>
<\/td>\\(\\sum f_i\\) = 30<\/td><\/td><\/td>\\(\\sum f_iu_i\\) = -1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

By step deviation method :<\/p>\n\n\n\n

Mean = a + \\(\\sum f_iu_i\\over \\sum f_i\\) \\(\\times\\) h = 0.10 + \\(-1\\over 30\\) \\(\\times\\) 0.04<\/p>\n\n\n\n

= 0.10 – 0.0013 = 0.0987<\/p>\n\n\n\n

= 0.099 ppm<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Concentration of \\(SO_2\\) (in ppm) Frequency 0.00 – 0.04 4 0.04 – 0.08 9 0.08 – 0.12 9 0.12 – 0.16 2 0.16 – 0.20 4 0.20 – 0.24 2 Solution : Let the assumed mean a = 0.10 Concentration of \\(SO_2\\) (in ppm) Frequency (\\(f_i\\)) Mid – Value (\\(x_i\\)) \\(u_i\\) = \\(x_i …<\/p>\n

To find out concentration of \\(SO_2\\) in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented below. Find the mean concentration of \\(SO_2\\) in the air.<\/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":"\nTo find out concentration of \\(SO_2\\) in the air (in parts per million, i.e. ppm), the data was collected for 30 localities in a certain city and is presented below. 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