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Question

If the mean of 1,7,5,3,4,4 is m and 3,2,4,2,3,3, p is m-1 and median is q, then the value of p and q will  be-


A
p=3,q=4
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B
p=4,q=3
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C
p=4,q=4
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D
p=4,q=2
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Solution

The correct option is D $$p = 4 , q = 2$$
$$\displaystyle \frac{1+7+5+3+4+4}{6}=m$$
$$\displaystyle m=\frac{24}{6}=4$$
and, $$\displaystyle \frac{3+2+4+2+3+3+p}{7}=m-1$$
    $$\displaystyle \frac{17+p}{7}=4-1$$
    17+p=21
          p=4
Now, median of 3,2,4,2,3,3,p, is q. Then, 
For                         n=7(odd)
                     Median$$\displaystyle =\frac{n+1}{2}$$th term
                      $$\displaystyle q=\left ( \frac{7+1}{2} \right )$$ th term
                      q = 4th term
                      q = 2
Hence,           $$p=  4$$
                      $$q = 2$$

Mathematics

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