Find the mean, median and mode of the following data:


Class



0 - 20



20 - 40



40 - 60



60 - 80



80 - 100



100 - 120



120 - 140



Frequency



6



8



10



12



6



5



3


To find mean, we will solve by direct method:


CLASS



MID - POINT(xi)



FREQUENCY(fi)



fixi



0 - 20



10



6



60



20 - 40



30



8



240



40 - 60



50



10



500



60 - 80



70



12



840



80 - 100



90



6



540



100 - 120



110



5



550



120 - 140



130



3



390



TOTAL




50



3120



We have got


Σfi = 50 & Σfixi = 3120


mean is given by





To find median,


Assume Σfi = N = Sum of frequencies,


h = length of median class,


l = lower boundary of the median class,


f = frequency of median class


and Cf = cumulative frequency


Lets form a table.


CLASS



FREQUENCY(fi)



Cf



0 - 20



6



6



20 - 40



8



6 + 8 = 14



40 - 60



10



14 + 10 = 24



60 - 80



12



24 + 12 = 36



80 - 100



6



36 + 6 = 42



100 - 120



5



42 + 5 = 47



120 - 140



3



47 + 3 = 50



TOTAL



50




So, N = 50


N/2 = 50/2 = 25


The cumulative frequency just greater than (N/2 = ) 25 is 36, so the corresponding median class is 60 - 80 and accordingly we get Cf = 24(cumulative frequency before the median class).


Now, since median class is 60 - 80.


l = 60, h = 20, f = 12, N/2 = 25 and Cf = 24


Median is given by,




= 60 + 1.67


= 61.67


And we know that,


Mode = 3(Median) – 2(Mean)


= 3(61.67) – 2(62.4)


= 185.01 – 124.8


= 60.21


Hence, mean is 62.4, median is 61.67 and mode is 60.21.


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