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Standard IX

Mathematics

Properties of Measures of Central Tendency

If the mean o...

Question

If the mean of $x_{1}$ and $x_{2}$ is $M_{1},$ and that of $x_{1}, x_{2},$ $x_{3}, x_{4}$ is $M_{2},$ the mean of $x_{1}, x_{2}, x_{3} + a, x_{4} - a$ is

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Solution

Mean of $x_{1}, x_{2}$ is $M_{1}$

Mean of $x_{1}, x_{2}, x_{3}, x_{4}$ is $M_{2}$
$⟹ x_{1} + x_{2} + x_{3} + x_{4} = 4 M_{2}$

The mean of $x_{1}, x_{2}, x_{3} + a, x_{4} - a$ is
$\frac{x_{1}, x_{2}, x_{3} + a, x_{4} - a}{4} \frac{x_{1} + x_{2} + x_{3} + x_{4}}{4} \frac{4 M_{2}}{4} = M_{2}$

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If the mean of x1 and x2 is M1, and that of x1,x2, x3,x4 is M2, the mean of x1,x2,x3+a,x4−a is

Mean of x1,x2 is M1Mean of x1,x2,x3,x4 is M2⟹x1+x2+x3+x4=4M2The mean of x1,x2,x3+a,x4−a is x1,x2,x3+a,x4−a4x1+x2+x3+x444M24=M2

If the mean of $x_{1}$ and $x_{2}$ is $M_{1},$ and that of $x_{1}, x_{2},$ $x_{3}, x_{4}$ is $M_{2},$ the mean of $x_{1}, x_{2}, x_{3} + a, x_{4} - a$ is

Mean of $x_{1}, x_{2}$ is $M_{1}$

Mean of $x_{1}, x_{2}, x_{3}, x_{4}$ is $M_{2}$
$⟹ x_{1} + x_{2} + x_{3} + x_{4} = 4 M_{2}$

The mean of $x_{1}, x_{2}, x_{3} + a, x_{4} - a$ is
$\frac{x_{1}, x_{2}, x_{3} + a, x_{4} - a}{4} \frac{x_{1} + x_{2} + x_{3} + x_{4}}{4} \frac{4 M_{2}}{4} = M_{2}$