The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency is 50. Compute the missing frequency.


Class:



0-20



20-40



40-60



60-80



80-100



100-120



Frequency:



5



f1



10



f2



7



8



Class interval



Mid value (xi)



Frequency (fi)



fiui



0-20



10



5



50



20-40



30



f1



30f1



40-60



50



10



500



60-80



70



f2



70f2



80-100



90



7



630



100-120



110



8



880





N = 50



∑fiui = 30f1 + 70f2 + 2060



Given, Sum of frequency = 50


5+ f1 + 10 + f2 + 7 + 8 = 50


f1 + f2 = 50 – 5 – 10 – 7 – 8


f1 + f2 = 20


3f1 + 3f2 = 60 (i) [Multiply by 3]


And mean = 62.8


= 62.8


= 62.8


30f1 + 70f2 = 3140 – 2060


30f1 + 70f2 = 1080


3f1 + 7f2 = 108 (ii) [Divide by 10]


Subtract (i) from (ii), we get


3f1 + 7f2 – 3f1 – 3f2 = 108 – 60


4f2 = 48


f2 = 12


Put value of f2 in (i), we get


3f1 + 3 * 12 = 60


3f1 + 36 = 60


3f1 = 24


f1 = 8


So, f1 = 8 and f2 = 12


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