Question

If the median of the observations x, 3x, 5x and 7x is 12, then
find the mean of them.​

Answer 1

median of this is XXX....

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Answer 2

The mean of the given observation is 12.

Step-by-step explanation:

Let x be a natural number.

The given observations are :

x, 3x, 5x and 7x.

If x is a natural number than x <2x < 3x < 7x.

Since there are 4 observations  and 4 is even .

Thus , the median of the observations will be :

Median = Mean of middle two terms

$\Rightarrow\ 12=\dfrac{3x+5x}{2}\Rightarrow\ \dfrac{8x}{2}=12\\\\\Rightarrow\ 4x= 12\\\\\Rightarrow\ x=3$

It means the observations are 3, 3(3), 5(3) and 7(3).

i.e. 3 , 9 , 15 , 21

Mean of the observations = $\dfrac{\text{Sum of observations}}{\text{Number of observations}}$

$=\dfrac{3+9+15+21}{4}\\\\=\dfrac{48}{4}=12$

Hence, the mean of the given observation is 12.

# Learn more :

If the mean of two consecutive numbers is 10 find them

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