Question

Find the mean of first five composite numbers ?

Answer 1

Hint: In the given question, we are required to find out the mean of the first five composite numbers. A composite number is a positive integer that can be formed by multiplying two smaller positive integers. First, we have to find the first five composite numbers. Then, we have to calculate the mean of those numbers using the standard formula and method to calculate the mean or average.

Complete step by step answer:
Composite numbers are the numbers that have at least one divisor other than $1$ and itself. So, the first five composite numbers are: $4$, $6$, $8$, $9$, $10$ as all these numbers have smaller positive integers as their factors and thus have at least one divisor other than $1$ and themselves.
Now, we have to calculate the mean of the numbers: $4$, $6$, $8$, $9$, $10$.
Mean of n observations can be calculated easily by using the formula $\bar X = \dfrac{{\sum {{x_i}} }}{n}$ where ${x_i}$’s are the observations and n is the total number of observations. In other words, the mean of n observations can be calculated by simply adding all the numbers and then dividing their sum by the number of observations, n.
Now, \[\bar X = \left( {\dfrac{{4 + 6 + 8 + 9 + 10}}{5}} \right)\]
Doing the calculations and simplifying further, we get,
\[ \Rightarrow \bar X = \dfrac{{37}}{5}\]
\[ \Rightarrow \bar X = 7.4\]

So, the mean of first five composite numbers is \[7.4\].

Note: Mean is the average value of a data set consisting of various observations. The calculation of mean or average is very simple and basic. It is a measure of central tendency that is based on all the observations and presents a simple and systematic description of the data and forms the basis of a statistical analysis.