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CBSE Class 11-commerce Answered

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Asked by mukulbhardwaj2000 | 14 Jan, 2019, 04:19: PM
answered-by-expert Expert Answer
Class marks
No. Of Students
(Cumulative frequency)
Frequency
fi
middle value
mi
fi×mi
10 to <20 140 7 15 105
20 to <30 133 15 25 375
30 to <40 118 18 35 630
40 to <50 100 25 45 1125
50 to <60 75 30 55 1650
60 to <70 45 20 65 1300
70 to <80 25 16 75 1200
80 to <90 9 7 85 595
90 to <100 2 2 95 190
         
 
mean = begin mathsize 12px style fraction numerator begin display style sum from i equals 1 to 9 of f subscript i m subscript i end style over denominator begin display style sum from i equals 1 to 9 of f subscript i end style end fraction space equals space 7170 over 140 space equals space 51.21 end style
To get median, let us make the frquency and cumulative frequency table in ascending order of marks as shown below
Class Marks frequency
Cumulative
Frequency
10 to <20 7 7
20 to <30 15 22
30 to <40 18 40
40 to <50 25 65
50 to <60 30 95
60 to <70 20 115
70 to <80 16 131
80 to <90 7 138
90 to <100 2 140
 
since number of students n = 140, median class is the class that has marks in the range 50 to 60.
 
median = begin mathsize 12px style l space plus space fraction numerator open parentheses begin display style n over 2 end style minus c f close parentheses over denominator f end fraction cross times h space space equals space space 50 space plus fraction numerator open parentheses 70 minus 65 close parentheses over denominator 30 end fraction cross times 10 space equals space 51.66 end style
where l is lower limit of median class, n is total number of students, cf is cumulative frequency of preceeding median class ,
f is the frequency of median class and h is class width
 
Modal class is the class that has highest frequency.  Hence the class that has marks in the range of 50 to 60 is the modal class
because that has the highest frequency 30.
 
mode = begin mathsize 12px style equals space l space plus space fraction numerator f subscript 1 space minus space f subscript o over denominator 2 f subscript 1 space minus space f subscript 0 space minus space f subscript 2 end fraction space cross times h space equals space 50 space plus space fraction numerator open parentheses 30 minus 25 close parentheses over denominator open parentheses 60 minus 25 minus 20 close parentheses end fraction cross times 10 space equals space 53.33 end style
where l is lower limit of median class and h is width of class. f1 , fo and f2 are frquencies of median class, preceeding class to median class
and suceeding class to median class respectively
Answered by Thiyagarajan K | 15 Jan, 2019, 01:13: PM

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