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The mode
Merits
i. This can be determined from incomplete data given the observations along with the highest frequency are already known
ii. The mode has some applications in business
iii. The mode can be simply defined
iv. This can be determined simply from a graph
Demerits
i. If the data is quite ungrouped and large, determination of the mode can be rather cumbersome
ii. Employ of the formula to calculate the mode is unfamiliar to most business people
iii. The mode may occasionally be non-existent or there may be two modes for a described set of data. Hence in such a case a single mode may not exist
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f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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