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the marks obtained by 120 students in mathematics test is given in following distribution maks obtained 0-20
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Asked by rekhasharma25204 | 06 May, 2020, 07:42: PM
answered-by-expert Expert Answer
Question: The marks obtained by 120 students in mathematics test is given in the following distribution:
Marks obtained 0-20 20-40 40-60 60-80 80-100 Total
No. of students 17 f1 32 f2 19 120
The number of students in the mark groups 20-40 and 60-80 are f1 and f2 respectively. Find f1 and f2 if the mean marks is 50.
Solution:
Marks obtained      xi            fi                            fixi     
0-20 10  17                       170
20-40 30   f1                       30f1
40-60 50  32                     1600
60-80 70  f2                      70f2
80-100 90  19                     1710
   

sum from i equals 1 to 5 of f subscript i equals 120 equals 68 plus f subscript 1 plus f subscript 2 rightwards double arrow f subscript 1 plus f subscript 2 equals 52 space space... space left parenthesis i right parenthesis x with bar on top equals fraction numerator sum from i equals 1 to 5 of f subscript i x subscript i over denominator sum from i equals 1 to 5 of f subscript i end fraction rightwards double arrow 50 equals fraction numerator 3480 plus 30 f subscript 1 plus 70 f subscript 2 over denominator 120 end fraction rightwards double arrow 50 equals fraction numerator 348 plus 3 f subscript 1 plus 7 f subscript 2 over denominator 12 end fraction rightwards double arrow 600 equals 348 plus 3 f subscript 1 plus 7 f subscript 2 rightwards double arrow 3 f subscript 1 plus 7 f subscript 2 equals 252 M u l t i p l y i n g space left parenthesis i right parenthesis space b y space 3 space a n d space s u b t r a c t i n g space left parenthesis i i right parenthesis 3 f subscript 1 plus 3 f subscript 2 equals 156 3 f subscript 1 plus 7 f subscript 2 equals 252 rightwards double arrow negative 4 f subscript 2 equals negative 96 rightwards double arrow f subscript 2 equals 24 therefore space f subscript 1 equals 52 minus 24 equals 28 H e n c e comma space f subscript 1 equals 28 space a n d space f subscript 2 equals 24.

Answered by Renu Varma | 09 May, 2020, 12:59: PM

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