(B) The mean deviation of a distribution is minimum when it is taken about the median of the distribution.Given the observations are $x_1 < x_2 < \dot

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(B) The mean deviation of a distribution is minimum when it is taken about the median of the distribution.Given the observations are $x_1 The median of $n$ observations is the $\left( \frac{n+1}{2} \right)^{th}$ observation.For $n = 101$,the median is the $\left( \frac{101+1}{2} \right)^{th} = 51^{st}$ observation.Therefore,$k = x_{51}$.

Class 11 Mathematics Statistics Mean and Median

Medium

For a distribution $x_1, x_2, \dots, x_{101}$ such that $x_1 < x_2 < x_3 < \dots < x_{100} < x_{101}$,the mean deviation of this distribution about a number $k$ is minimum. Then $k$ is equal to which of the following?

A
$x_1$
B
$x_{51}$
C
$x_{50}$
D
$\frac{x_1 + x_2 + \dots + x_{101}}{101}$

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Class 11 Questions

Class 11

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Statistics

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Mean and Median

If the mean of $3, 4, x, 7, 10$ is $6$,then the value of $x$ is

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If ${d_i}$ is the deviation of a class mark ${y_i}$ from $a$,the assumed mean,and ${f_i}$ is the frequency,if ${M_g} = x + \frac{1}{{\sum {f_i}}}(\sum {f_i}{d_i})$,then $x$ is:

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The observations $29, 32, 48, 50, x, x + 2, 72, 78, 84, 95$ are arranged in ascending order. If their median is $63$,what is the value of $x$?

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If the values $1, \frac{1}{2}, \frac{1}{3}, \dots, \frac{1}{n}$ have frequencies $1, 2, 3, \dots, n$ respectively,what is their mean?

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If in an examination different weights are assigned to different subjects: Physics $(2)$,Chemistry $(1)$,English $(1)$,and Mathematics $(2)$. If a student scored $60$ in Physics,$70$ in Chemistry,$70$ in English,and $80$ in Mathematics,then his weighted $A.M.$ is:

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For a distribution $x_1, x_2, \dots, x_{101}$ such that $x_1 < x_2 < x_3 < \dots < x_{100} < x_{101}$,the mean deviation of this distribution about a number $k$ is minimum. Then $k$ is equal to which of the following?

Similar Questions

If the mean of $3, 4, x, 7, 10$ is $6$,then the value of $x$ is

If ${d_i}$ is the deviation of a class mark ${y_i}$ from $a$,the assumed mean,and ${f_i}$ is the frequency,if ${M_g} = x + \frac{1}{{\sum {f_i}}}(\sum {f_i}{d_i})$,then $x$ is:

The observations $29, 32, 48, 50, x, x + 2, 72, 78, 84, 95$ are arranged in ascending order. If their median is $63$,what is the value of $x$?

If the values $1, \frac{1}{2}, \frac{1}{3}, \dots, \frac{1}{n}$ have frequencies $1, 2, 3, \dots, n$ respectively,what is their mean?

If in an examination different weights are assigned to different subjects: Physics $(2)$,Chemistry $(1)$,English $(1)$,and Mathematics $(2)$. If a student scored $60$ in Physics,$70$ in Chemistry,$70$ in English,and $80$ in Mathematics,then his weighted $A.M.$ is:

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