Question

the mean of 6 observation is 15. four of the observation are 10,18,23 and 9. of the remaining two observation one is four times the other. find them​

Answer 1

Given :

The mean of 6 observation is 15. four of the observation are 10,18,23 and 9. of the remaining two observation one is four times the other.

To find :

• Remaining two observations

Solution :

★ Mean of 6 observation = 15

★ 4 observations = 10, 18, 23 & 9

★ Remaining two observations = One is four times the other.

Consider the first observation be x & the second observation be 4x

• As we know that

${\bold \dag}\:{\boxed{\pmb{\tt{\red{Mean=\dfrac{Sum \: of \: the \: total \: observations}{Number\: of\: the \: observations}}}}}}$

$\\ \implies \sf 15 = \dfrac{10 + 18 + 23 + 9 + x + 4x}{6} \\ \\ \implies \sf 15 = \dfrac{ 60 + 5x}{6} \\ \\ \implies \sf 90 = 60 + 5x \\ \\ \implies \sf 90 - 60 = 5x \\ \\ \implies \sf 5x = 30 \\ \\ \implies\sf x =\cancel\dfrac{30}{5}\\ \\ \therefore\sf x = 6$

Other two observations

• x = 6

• 4x = 4 × 6 = 24

Therefore, other two observations are 6 & 24

Answer 2

Answer:

Given :-

Mean of 6 observation = 15

Four observation = 10,18,23,9

To Find :-

The two numbers

Solution :-

Let the number be y and 4y

Now,

Mean = Sum of observation/Total number of observation

Mean = 10 + 18 + 23 + 9 + y + 4y/6

15 = 28 + 32 + 5y/6

15 × 6 = 60 + 5y

90 = 60 + 5y

90 - 60 = 5y

30 = 5y

30/5 = y

6 = y

Two observation are

y = 6

4y = 24