{"id":12629,"date":"2022-12-20T18:45:25","date_gmt":"2022-12-20T13:15:25","guid":{"rendered":"https:\/\/mathemerize.com\/?p=12629"},"modified":"2022-12-20T18:45:30","modified_gmt":"2022-12-20T13:15:30","slug":"the-following-frequency-distribution-gives-the-monthly-consumption-of-electricity-of-68-consumers-of-a-locality-find-the-median-and-mode-of-the-data-and-compare-them","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-following-frequency-distribution-gives-the-monthly-consumption-of-electricity-of-68-consumers-of-a-locality-find-the-median-and-mode-of-the-data-and-compare-them\/","title":{"rendered":"The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median and mode of the data and compare them."},"content":{"rendered":"\n

Question :<\/h2>\n\n\n\n
Monthly Consumption<\/td>65 – 85<\/td>85 – 105<\/td>105 – 125<\/td>125 – 145<\/td>145 – 165<\/td>165 – 185<\/td>185 – 205<\/td><\/tr>
Number of Consumers<\/td>4<\/td>5<\/td>13<\/td>20<\/td>14<\/td>8<\/td>4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Solution :<\/h2>\n\n\n\n
Monthly Consumption of Electricity<\/td>No. of Consumers<\/td>Less than type cumulative frequency<\/td><\/tr>
65 – 85<\/td>4<\/td>4<\/td><\/tr>
85 – 105<\/td>5<\/td>9<\/td><\/tr>
105 – 125<\/td>13<\/td>22 = C<\/td><\/tr>
125 – 145<\/td>20 = f<\/td>42<\/td><\/tr>
145 – 165<\/td>14<\/td>56<\/td><\/tr>
165 – 185<\/td>8<\/td>64<\/td><\/tr>
185 – 205<\/td>4<\/td>68<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Since \\(68\\over 2\\) belongs to the cumulative frequency (42) of the class interval (125 – 145) therefore, it is the median class interval.<\/p>\n\n\n\n

Lower limit of the median class interval = l = 125<\/p>\n\n\n\n

Width of the class interval = h = 20<\/p>\n\n\n\n

Total frequency = N = 68<\/p>\n\n\n\n

Cumulative frequency preceding median class frequency = C = 22<\/p>\n\n\n\n

Frequency of the median class = f = 20<\/p>\n\n\n\n

Median = l + (\\({N\\over 2} – C\\over f\\))(h) = 125 + \\(12\\times 20\\over 20\\) = 125 + 12 = 137<\/strong><\/p>\n\n\n\n

The frequency of class (125 – 145) is maximum i.e. 20, this is the modal class.<\/p>\n\n\n\n

\\(x_k\\) = 125, \\(f_k\\) = 20, \\(f_{k – 1}\\) = 13, \\(f_{k + 1}\\) = 14, h = 20<\/p>\n\n\n\n

Mode = \\(x_k\\) + \\(f – f_{k – 1}\\over 2f – f_{k – 1} – f_{k + 1}\\) = 125 + \\(20 – 13\\over 40 – 13 – 14\\)\\(\\times\\) 20<\/p>\n\n\n\n

= 120 + \\(7\\over 13\\) \\(\\times\\) 20 = 125 + 10.77 = 135.77<\/strong> <\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Monthly Consumption 65 – 85 85 – 105 105 – 125 125 – 145 145 – 165 165 – 185 185 – 205 Number of Consumers 4 5 13 20 14 8 4 Solution : Monthly Consumption of Electricity No. of Consumers Less than type cumulative frequency 65 – 85 4 4 85 …<\/p>\n

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median and mode of the data and compare them.<\/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 frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. 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