Question

If the mean of x, x+3,x+6,x+9,x+12,x+15.is 18 find the mean of first four observation​

Answer 1

Given :

• Given observations = x,(x + 3),(x + 6),(x + 9),(x + 12),(x + 15).

• Mean of all the observations = 18.

• No. if term = 6

To find :

Mean of first four observations.

Solution :

We know the formula for mean,i.e,

$\boxed{\bf{Mean = \dfrac{\Sigma x_{i}}{n}}}$

Where :

• $\bf{\Sigma x_{i}}$ = Sum of all observations.

• $\bf{n}$ = No. of all observations.

By using the formula for mean and substituting the values in it, we get :

$:\implies \bf{Mean = \dfrac{\Sigma x_{i}}{n}}$

$:\implies \bf{Mean = \dfrac{x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6}}{n}}$

$:\implies \bf{18 = \dfrac{x + (x + 3) + (x + 6) + (x + 9) + (x + 12) + (x + 15)}{6}}$

$:\implies \bf{18 = \dfrac{(x + x + x + x + x + x) + (3 + 6 + 9 + 12 + 15)}{6}}$

$:\implies \bf{18 = \dfrac{6x + 45}{6}}$

$:\implies \bf{18 \times 6 = 6x + 45}$

$:\implies \bf{108 = 6x + 45}$

$:\implies \bf{108 - 45 = 6x}$

$:\implies \bf{63 = 6x}$

$:\implies \bf{\dfrac{63}{6} = x}$

$:\implies \bf{10.5 = x}$

$\boxed{\therefore \bf{x = 10.5}}$

Hence the value of x 10.5.

From the above equation , we get :

• First term = x = 10.5

• Second term = (x + 3) = 13.5

• Third term = (x + 6) = 16.5

• Fourth term = (x + 9) = 19.5

• Fifth term = (x + 12) = 22.5

• Sixth term = (x + 15) = 25.5

Now to find the mean of first four terms of the observation.

$\boxed{\bf{Mean = \dfrac{\Sigma x_{i}}{n}}}$

Where :

• $\bf{\Sigma x_{i}}$ = Sum of all observations.

• $\bf{n}$ = No. of all observations.

By using the formula for mean and substituting the values in it, we get :

$:\implies \bf{Mean = \dfrac{\Sigma x_{i}}{n}}$

$:\implies \bf{Mean = \dfrac{x_{1} + x_{2} + x_{3} + x_{4}}{n}}$

$:\implies \bf{Mean = \dfrac{10.5 + 13.5 + 16.5 + 19.5}{4}}$

$:\implies \bf{Mean = \dfrac{10.5 + 13.5 + 16.5 + 19.5}{4}}$

$:\implies \bf{Mean = \dfrac{60}{4}}$

$:\implies \bf{Mean = 15}$

$\boxed{\therefore \bf{Mean = 15}}$

Hence the mean of first four terms of the observation is 15.