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is this question right ?  if yes then how to find value "a" ? 
question image
Asked by riturajrahul.ahirwar434 | 16 Feb, 2019, 19:37: PM
answered-by-expert Expert Answer
Given distribution of data is multi modal.
Hence finding the mode by observing for the highest frequency is not possible in the given data.
 
Hence mode is obtained from the formula   " mode = 3×median - 2×mean "
 
data x 42 46 49 51 55 a 56
frequency f
1 4 4 1 4 1 4
Cumulative
frequency cf
 1 5 9 10 14 15 19
mean = [ 42×1 + 46×4 + 49×4 + 51×1 + 55×4 + a×1 + 56×4 ] / 19 = (917+a)/19
 
median is the value where cumlative frequency is half  of total  frequency.
Let us take in this case median is at cumulative frequency 10. hence median is 51
 
hence  mode = 49 = 3×51 - 2× [ (917+a)/19 ]  ........................(1)
 
From the above eqn.(1), we get a = 52
Answered by Thiyagarajan K | 17 Feb, 2019, 12:56: PM

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