Question

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

Answer 1

Hint: Here we have to find the value of the unknown number. For that, we will first find the mean of all six numbers. We will find the mean by adding all six numbers including the unknown number and then we will divide the sum by total number of numbers. Then we will equate the calculated mean with the given mean. From there, we will get the value of the unknown number.

Complete step by step solution:
First we will apply the formula of the mean for these six numbers. We know that the mean is defined as the ratio of sum of terms to the total number of terms.
We will find the sum of these six numbers.
Therefore,
\[\begin{array}{l} \Rightarrow {\rm{Sum}} = 10 + 12 + 18 + 13 + P + 17\\ \Rightarrow {\rm{Sum}} = 70 + P\end{array}\]
Therefore, mean of six numbers 10, 12, 18, 13, \[P\] and 17 \[ = \dfrac{{{\rm{Sum}}}}{6}\]
Substituting the value of sum, we get
\[ \Rightarrow {\rm{mean}} = \dfrac{{70 + P}}{6}\] ……… \[\left( 1 \right)\]
Now, we will substitute the value of the given mean of these six numbers in equation \[\left( 1 \right)\]. Therefore, we get
\[ \Rightarrow 15 = \dfrac{{70 + P}}{6}\]
On cross multiplying the terms, we get
\[ \Rightarrow 15 \times 6 = 70 + P\]
Now, we will multiply 15 with 6 on the left hand side of the equation.
\[ \Rightarrow 90 = 70 + P\]
Subtracting 70 from both the sides, we get
\[ \Rightarrow 90 - 70 = 70 + P - 70\]
\[ \Rightarrow 20 = P\]
Hence, the required value of \[P\] is 20.

Note: Here we have used the formula of mean. A mean is also known as average and it is defined as the ratio of sum of all observations to the total number of observations.
Some important properties of mean are as follows:-
If we add the same number to each observation then their mean will also be increased by the same number.
If we subtract same number from each observation then their mean will also be decreased by the same number
If we multiply the same number to observation then their resultant mean will be the product of the earlier mean and the same multiplied number.