{"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
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\nSolution :<\/h2>\n\n\n\nThe 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 \\(\\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 |