(B) The mean deviation of a set of observations about a point $k$ is minimized when $k$ is the median of the observations.For a set of $n$ observation

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(B) The mean deviation of a set of observations about a point $k$ is minimized when $k$ is the median of the observations.For a set of $n$ observations arranged in ascending order,the median is the middle term.Here,$n = 101$,which is an odd number.The position of the median is given by $\frac{n + 1}{2} = \frac{101 + 1}{2} = 51$.Thus,the median is the $51^{st}$ observation,which is ${x_{51}}$.

Class 11 Mathematics Statistics Mean and Median

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Consider a set of observations ${x_1}, {x_2}, {x_3}, ..., {x_{101}}$ such that ${x_1} < {x_2} < {x_3} < ... < {x_{100}} < {x_{101}}$. The mean deviation of this set of observations about a point $k$ is minimum when $k$ equals:

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

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Class 11 Questions

Class 11

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Chapter

Statistics

Subtopic

Mean and Median

The following data gives the distribution of height of students:

Height (in $cm$) $160$ $150$ $152$ $161$ $156$ $154$ $155$

No of students $12$ $8$ $4$ $4$ $3$ $3$ $7$

The median of the distribution is:

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The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x, 42, 67, 70, y$ are $42$ and $35$ respectively. Then,$\frac{y}{x}$ is equal to:

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The median of $10, 14, 11, 9, 8, 12, 6$ is

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$A$ student obtains $75\%$,$80\%$,and $85\%$ in three subjects. If the marks of a fourth subject are added,then his average cannot be less than.....$\%$

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If a variable takes the discrete values $\alpha + 4, \alpha - \frac{7}{2}, \alpha - \frac{5}{2}, \alpha - 3, \alpha - 2, \alpha + \frac{1}{2}, \alpha - \frac{1}{2}, \alpha + 5$ where $\alpha > 0$,then the median of these values is:

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Height (in $cm$)	$160$	$150$	$152$	$161$	$156$	$154$	$155$
No of students	$12$	$8$	$4$	$4$	$3$	$3$	$7$

Consider a set of observations ${x_1}, {x_2}, {x_3}, ..., {x_{101}}$ such that ${x_1} < {x_2} < {x_3} < ... < {x_{100}} < {x_{101}}$. The mean deviation of this set of observations about a point $k$ is minimum when $k$ equals:

Similar Questions

The following data gives the distribution of height of students: Height (in $cm$) $160$ $150$ $152$ $161$ $156$ $154$ $155$ No of students $12$ $8$ $4$ $4$ $3$ $3$ $7$ The median of the distribution is:

The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x, 42, 67, 70, y$ are $42$ and $35$ respectively. Then,$\frac{y}{x}$ is equal to:

The median of $10, 14, 11, 9, 8, 12, 6$ is

$A$ student obtains $75\%$,$80\%$,and $85\%$ in three subjects. If the marks of a fourth subject are added,then his average cannot be less than.....$\%$

If a variable takes the discrete values $\alpha + 4, \alpha - \frac{7}{2}, \alpha - \frac{5}{2}, \alpha - 3, \alpha - 2, \alpha + \frac{1}{2}, \alpha - \frac{1}{2}, \alpha + 5$ where $\alpha > 0$,then the median of these values is:

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The following data gives the distribution of height of students:

Height (in $cm$) $160$ $150$ $152$ $161$ $156$ $154$ $155$

No of students $12$ $8$ $4$ $4$ $3$ $3$ $7$

The median of the distribution is: