Question

Find the mean of all factors of 10.

Answer 1

Hint: The mean is the average of the numbers. Use this formula to calculate mean. \[Mean(\overline{x})=\dfrac{Sum\,of\,all\,observations}{Total\,number\,of\,observations}\]

Complete step-by-step answer:
As we all know that, a factor divides the number completely without leaving a remainder.
Since 1 is the factor of all numbers and the number is factor of itself
\[\Rightarrow \] Factors of \[10=1,2,5,10\]
Only these numbers completely divide the \[10\]
Let the factors be \[{{x}_{i}}\]
\[\begin{align}
  & {{x}_{1}}=1 \\
 & {{x}_{2}}=2 \\
 & {{x}_{3}}=5 \\
 & {{x}_{4}}=10 \\
\end{align}\]
 \[\Rightarrow \] The total number of factors are \[4\]
Now we will calculate the Mean \[(\overline{x})\]:
\[Mean(\overline{x})=\dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}}{4}=\dfrac{1+2+5+10}{4}=\dfrac{18}{4}=4.5\]
Thus we have calculated the mean the of all factors of 10
Hence, the \[Mean(\overline{x})=4.5\]

Note: For a data set, the arithmetic mean, also called the expected value pr average is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.