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How much does a data set's mode exceed the median if the mode exceeds its mean by 9? 

Option: 1

6


Option: 2

8


Option: 3

9


Option: 4

10


Answers (1)

best_answer

option (A) 6

It is given that the mode of a data exceeds its mean by 9.

We know that by the empirical relationship formula of distribution,

\mathrm{\text{3Median = Mode + 2Mean}}............(1)

Let’s assume that the median of a data is M, the mode is m, and its mean is z.

According to the question, we have,

\mathrm{\ {m=z+9} }

\mathrm{\Rightarrow {z=m-\ 9}}.......(2)

Now, using equation (2) in equation (1), we get,

\mathrm{ \ {3M=m+2z}}

\mathrm{ \ {3M=m+2(m-\ 9)}}

\mathrm{ \ {3M=3m-\ 18}}

\mathrm{ \ {(3M+6)= 3m}}

\mathrm{ \ {(M+6)= m}}

So, mode exceeds median by 6.

Posted by

Shailly goel

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