{"id":12357,"date":"2022-10-22T22:48:27","date_gmt":"2022-10-22T17:18:27","guid":{"rendered":"https:\/\/mathemerize.com\/?p=12357"},"modified":"2022-10-22T22:48:31","modified_gmt":"2022-10-22T17:18:31","slug":"the-following-distribution-gives-the-step-wise-teacher-student-ration-in-higher-secondary-schools-of-india-find-the-mode-and-mean-of-this-data-interpret-the-two-measures","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-following-distribution-gives-the-step-wise-teacher-student-ration-in-higher-secondary-schools-of-india-find-the-mode-and-mean-of-this-data-interpret-the-two-measures\/","title":{"rendered":"The following distribution gives the step-wise teacher-student ration in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures."},"content":{"rendered":"\n

Question :<\/h2>\n\n\n\n
Number of students per teacher<\/td>Number of states\/U.T.<\/td><\/tr>
15 – 20<\/td>3<\/td><\/tr>
20 – 25<\/td>8<\/td><\/tr>
25 – 30<\/td>9<\/td><\/tr>
30 – 35<\/td>10<\/td><\/tr>
35 – 40<\/td>3<\/td><\/tr>
40 – 45<\/td>0<\/td><\/tr>
45 – 50<\/td>0<\/td><\/tr>
50 – 55<\/td>2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

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

The class (30 – 35) has the maximum frequency. Therefore, this is the modal class.<\/p>\n\n\n\n

Here, l = 30, h = 5, \\(f_1\\) = 10, \\(f_0\\) = 9 and \\(f_2\\) = 3.<\/p>\n\n\n\n

Now, let us substitute these values 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

Mode = 30 + \\(10 – 9\\over 20 – 9 – 3\\) \\(\\times\\) 5<\/p>\n\n\n\n

Mode = 30 + 0.625 = 30.625<\/strong><\/p>\n\n\n\n

Calculation of mean :<\/p>\n\n\n\n

Number of students per teacher<\/td>Number of states\/U.T.<\/td>Mid-point (\\(x_i\\)<\/td>\\(f_iu_i\\)<\/td><\/tr>
15 – 20<\/td>3<\/td>17.5<\/td>52.5<\/td><\/tr>
20 – 25<\/td>8<\/td>22.5<\/td>180.0<\/td><\/tr>
25 – 30<\/td>9<\/td>27.5<\/td>247.5<\/td><\/tr>
30 – 35<\/td>10<\/td>32.5<\/td>325.0<\/td><\/tr>
35 – 40<\/td>3<\/td>37.5<\/td>112.5<\/td><\/tr>
40 – 45<\/td>0<\/td>42.5<\/td>0<\/td><\/tr>
45 – 50<\/td>0<\/td>47.5<\/td>0<\/td><\/tr>
50 – 55<\/td>2<\/td>52.5<\/td>105.5<\/td><\/tr>
Total<\/td>35<\/td>40<\/td>1022.5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\\(\\bar{x}\\) = \\(\\sum f_ix_i\\over \\sum f_i\\) = \\(1022.5\\over 35\\) = 29.2<\/p>\n\n\n\n

Mean = 29.2<\/strong><\/p>\n\n\n\n

Thus, most states\/U.T have a student teacher ration of 30.6 and on average, the ratio is 29.2<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Number of students per teacher Number of states\/U.T. 15 – 20 3 20 – 25 8 25 – 30 9 30 – 35 10 35 – 40 3 40 – 45 0 45 – 50 0 50 – 55 2 Solution : The class (30 – 35) has the maximum frequency. Therefore, this …<\/p>\n

The following distribution gives the step-wise teacher-student ration in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.<\/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 distribution gives the step-wise teacher-student ration in higher secondary schools of India. Find the mode and mean of this data. 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