By Manoj K. Bhowal and Pronob Barua
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Extra resources for Statistics Volume 1 (Second Edition)
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30 12 8 Solution: Let the missing frequency be J;. Marks No. 9 .. 12 = 15 [since frequency can not be in fraction] Statistics 38 Example 6 : If the relation between the variables x and y is 2x - 3y + 4 and y = 6, then what will be the value of =0 x? Solution: If 2x - 3y + 4=0 => 3y= 2x + 4 => 3y=2x+4 Now Y == 6 .. 18=2x +4 2x=18-4 => x =7 => Example 7 : The mean salary paid to 1000 employees of an establishment was found to be Rs. 40. Later on, after disbursement of salary, it was discovered that the salary of two employees was wrongly entered as Rs.
Iv) It is useful in calculating rates. Demerits: (i) It is not easy to understand and calculate. (ii) It cannot be calculated if value of any item is zero. Example 27 : Prove that (i) AM~GM~HM 55 Measures o/Central Tendency (ii) AM x HM = (GM)l Solution: We shall prove the result for two observations only. The result can be generalized for any number of observations. Letx l and x2 be two real numbers which are non-zero and non-negative. jX I X 2 (I I ')2 lrx;-J;;J ~ ... (i) 0 => => GM~HM Thus from (i) and (ii) we get, AM (ii) LHS = AM x HM = XI +X2 2 ...
He frequency distribution of marks of 100 students. tarks No. of Students Marks No. of Students 2;)-29 7 60-69 9 30-39 14 11 70-79 LlO-il9 24 80-89 2 50-59 32 90-99 Draw less than ogive and use it to' determine median. 29 Frequency Distribution and Graphical Representation 19. Draw a histogram and frequency curve from the following data 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Marks: No. of students: 4 8 11 15 12 7 3 (AHSEC 2008) 20. ) 10-15 15-20 20-25 25-30 No. of workers: 40 120 190 150 (AHSEC 2007) 21.