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Question

Mathematics Question on Mean Deviation

The mean deviation about the median for the data 3,5,9,3,8,10,73,5,9,3,8,10,7 is ?

A

237\dfrac{23}{7}

B

47\dfrac{4}{7}

C

−47\dfrac{-4}{7}

D

167\dfrac{16}{7}

E

177\dfrac{17}{7}

Answer

167\dfrac{16}{7}

Explanation

Solution

Given data:

Mean deviation about the median data= 3,5,9,3,8,10,73,5,9,3,8,10,7

arranging it in ascending order =3,3,5,7,8,9,10 3,3,5,7,8,9,10

Hence observation(nn)=77

median=n+12=7+12=4\dfrac{n+1}{2}=\dfrac{7+1}{2}=4

Now, the mean deviation about the median= ∣3−7∣+∣3−7∣+∣5−7∣+∣7−7∣+∣8−7∣+∣9−7∣+∣10−7∣​7\dfrac{|3−7∣+|3−7|+|5−7|+|7−7|+|8−7|+∣9−7∣+∣10−7∣​}{7}

                                                        =$\dfrac{16}{7}$ (_Ans.)