the median and modal profits for the following data
profit in 000 rs. below 5 below 10 below 15 below 20 below 25 below 30
no. of firms 10 25 45 55 62 65
answer:
i) 11.60 and 11.50
ii) 11556 and 11267
iii) 11875 and 11667
iv) 11.50 and 11.67
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Replies (1)
First convert the cumulative less than type frequency distribution into a simple continuous frequency distribution as follows
0 - 5 : 10, 5 - 10 : 15, 10 - 15 : 20, 15 -20 : 10, 20 - 25 : 7, 25 - 30 : 7
Then calculate the median class which is 10 - 15, then apply the formula of median based on interpolation as given below :
Md = L + (N/2 - C.F.) / F x i = 11.875 ( in thousands)
Mo = L + (F1 - F0) / (2F1 - F0 - F2) x i = 11.666 ( in thousands)
Hence option iii is correct
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