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 $$\text{Mean}={\displaystyle \frac{\text{Sum of all n numbers}}{n}}.$$ 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.
$$\text{Mean}={\displaystyle \frac{\text{Sum of first 5 natural numbers}}{5}}$$
$$\Rightarrow \text{Mean}={\displaystyle \frac{1+2+3+4+5}{5}}$$
$$\Rightarrow \text{Mean}={\displaystyle \frac{15}{5}}$$
$$\Rightarrow \text{Mean}=3$$
Similarly, we will calculate the mean of 6, 4, 7, p and 10. Using the formula of mean, we have,
$$\text{Mean}={\displaystyle \frac{\text{Sum of all terms}}{\text{Number of the terms}}}$$
$$\Rightarrow \text{Mean}={\displaystyle \frac{6+4+7+p+10}{5}}$$
$$\Rightarrow \text{Mean}={\displaystyle \frac{27+p}{5}}$$
Given that the mean of 6, 4, 7, p and 10 is 8.
$$\Rightarrow \text{Mean}=8={\displaystyle \frac{27+p}{5}}$$
Considering the RHS of the above equation, we have,
$$\Rightarrow 8={\displaystyle \frac{27+p}{5}}$$
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.