Question

If the mean of 10. 12. 18. 13. P and 17 is 15. find the value of P? ​

Answer 1

Answer:

Given :-

• The mean of 10, 12, 18, 13, P and 17 is 15.

To Find :-

• What is the value of p.

Formula Used :-

$\clubsuit$ Mean Formula :

$\small \bigstar \: \: \sf\boxed{\bold{Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}}}\: \: \: \bigstar$

Solution :-

Given :

• Mean = 15
• Sum of all observations = 10, 12, 18, 13, P, 17
• Total Number of Observations= 5

According to the question by using the formula we get,

$\small \implies \bf Mean =\: \dfrac{Sum\: of\: Observations}{Total\: Number\: of\: Observations}$

$\implies \sf 15 =\: \dfrac{10 + 12 + 18 + 13 + P + 17}{6}$

$\implies \sf 15 =\: \dfrac{22 + 18 + 13 + P + 17}{6}$

$\implies \sf 15 =\: \dfrac{40 + 13 + P + 17}{6}$

$\implies \sf 15 =\: \dfrac{53 + P + 17}{6}$

$\implies \sf 15 =\: \dfrac{53 + 17 + P}{6}$

$\implies \sf 15 =\: \dfrac{70 + P}{6}$

By doing cross multiplication we get,

$\implies \sf 70 + P =\: 15(6)$

$\implies \sf 70 + P =\: 15 \times 6$

$\implies \sf 70 + P =\: 90$

$\implies \sf P =\: 90 - 70$

$\implies \sf\bold{P =\: 20}$

$\sf\bold{\underline{\therefore\: The\: value\: of\: P\: is\: 20\: .}}$

Answer 2

Given:-

• Numbers:- 10,12,18,13,P and 17.
• Mean=15.

To find:-

• Value of P.

Formula used:-

$\small\green{\underline{ \blue{\boxed{\bf{ \red{Mean= \frac{Sum\: of \: Observations}{Number \: of \: observations} }}}}}}$

Solution:-

In the question it is given as the given numbers have mean as 15 and the number of observations are 6 .We can calculate the value of P easily and efficiently with the formula.

$\large{\sf{ \implies15= \frac{10 + 12 + 18 + 13 + 17 +P }{6} }}$

$\large{\sf{15 = \frac{70 + P}{6} }}$

$\large{\sf{ \implies15 \times 6 = 70+P}}$

$\large{\sf{ \implies90 = 70 +P }}$

$\large{\sf{90-70=P}}$

$\large \green{\underline{ \pink{\boxed{\bf{ \red{20=P}}}}}}$

Hence the value of P is 20.

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Additional information!!

• Mean is (sum of observations/Number of observations)
• Mean is also known as Average.
• Median is the middle term of the observations.
• Mode is that term which appears most time in the observations.
• Range is that value which we gets after subtracting lowest term from largest term.