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Mean Deviation about Median

Consider any ...

Question

Consider any set of 201 observations $x_{1}, x_{2}, \dots, x_{200}, x_{201}$ . It is given that $x_{1} < x_{2} < \dots < x_{200} < x_{201}$ . Then, the mean deviation of this set of observations about a point k is minimum, when k equals

$\frac{x_{1} + x_{2} + \dots + x_{200} + x_{201}}{201}$

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$x_{1}$

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$x_{101}$

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$x_{201}$

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Solution

The correct option is C
$x_{101}$

$x_{1} < x_{2} < x_{3} < \dots < x_{201}$
$∴$ Median of the given observation $= {(\frac{201 + 1}{2})}^{th}$ item $= x_{101}$
Now, deviations will be minimum, if taken from the median.
$∴$ Mean deviation will be minimum, if k $= x_{101}$

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Similar questions

Consider any set of 201 observations $x_{1}, x_{2}, \dots, x_{200}, x_{201}$ . It is given that $x_{1} < x_{2} < \dots < x_{200} < x_{201}$ . Then, the mean deviation of this set of observations about a point k is minimum, when k equals

Q. Consider set of observations

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x_{1} < x_{2} < x_{3} \dots < x_{100} < x_{101}

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is minimum when

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______________.

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Consider any set of 201 observations x1, x2, ⋯,x200, x201. It is given that x1<x2<⋯<x200<x201. Then, the mean deviation of this set of observations about a point k is minimum, when k equals

The correct option is C x101 x1<x2<x3<⋯<x201 ∴ Median of the given observation =(201+12)th item =x101 Now, deviations will be minimum, if taken from the median. ∴ Mean deviation will be minimum, if k =x101

Consider any set of 201 observations $x_{1}, x_{2}, \dots, x_{200}, x_{201}$ . It is given that $x_{1} < x_{2} < \dots < x_{200} < x_{201}$ . Then, the mean deviation of this set of observations about a point k is minimum, when k equals

The correct option is C
$x_{101}$

$x_{1} < x_{2} < x_{3} < \dots < x_{201}$
$∴$ Median of the given observation $= {(\frac{201 + 1}{2})}^{th}$ item $= x_{101}$
Now, deviations will be minimum, if taken from the median.
$∴$ Mean deviation will be minimum, if k $= x_{101}$