Question

If the mean of 6, 4, 7, p and 10 is 8, find the value of p.

Answer 1

Hint: To solve this question, we will use the formula of calculating the mean of some numbers of the data given. The mean of n numbers is given by \[\text{Mean}=\dfrac{\text{Sum of all n numbers}}{n}.\] Therefore, we will use this formula to calculate the value of p.

Complete step by step answer:
Let us first define the mean. Mean is also called the Arithmetic Mean n the average of the numbers also called a central value of a set of numbers. To calculate mean,
1. Add up all the numbers
2. Then divide by how many numbers there are.
Example: Calculate the mean of the first 5 natural numbers. The first five natural numbers are 1, 2, 3, 4, 5.
\[\text{Mean}=\dfrac{\text{Sum of first 5 natural numbers}}{5}\]
\[\Rightarrow \text{Mean}=\dfrac{1+2+3+4+5}{5}\]
\[\Rightarrow \text{Mean}=\dfrac{15}{5}\]
\[\Rightarrow \text{Mean}=3\]
Similarly, we will calculate the mean of 6, 4, 7, p and 10. Using the formula of mean, we have,
\[\text{Mean}=\dfrac{\text{Sum of all terms}}{\text{Number of the terms}}\]
\[\Rightarrow \text{Mean}=\dfrac{6+4+7+p+10}{5}\]
\[\Rightarrow \text{Mean}=\dfrac{27+p}{5}\]
Given that the mean of 6, 4, 7, p and 10 is 8.
\[\Rightarrow \text{Mean}=8=\dfrac{27+p}{5}\]
Considering the RHS of the above equation, we have,
\[\Rightarrow 8=\dfrac{27+p}{5}\]
Multiplying by 5 on both the sides, we get,
\[\Rightarrow 40=27+p\]
\[\Rightarrow 27+p=40\]
\[\Rightarrow p=40-27\]
\[\Rightarrow p=13\]

So, the value of p is 13.

Note: Do not forget to add p on counting the number of terms for writing the denominator of the mean formula. The given terms are 6, 4, 7 and 10, but p is also one of them. Therefore, the number of terms will be 5 and not 4, even if we have to calculate the value of p. Also, note that the Arithmetic mean and mean are the same here.