Question

The mean of the first eight prime numbers is $\dfrac{{{\text{77}}}}{{\text{8}}}$.
$\left( {\text{A}} \right)$ True
$\left( {\text{B}} \right)$ False

Answer 1

Hint: First, we have to know about prime numbers.
Then we find out the mean value of first eight prime number by using the formula
Mean value is nothing but the average value.
Finally we get the required answer.

Formula used: Mean or Average $ = \dfrac{{{\text{sum of all values}}}}{{{\text{number of values}}}}$

Complete step-by-step solution:
Prime number are natural numbers greater than $1$ that have only two factors there are $1$ and the number itself.
In other words, prime numbers are divisible only by the number $1$ and itself.
For instance, we can take $3$ as a prime number.
Because it can be divided only by itself and one.
On the other hand, $6$ can be divided evenly by ${\text{1, 2, 3 and 6}}$ .
So it is not a prime number.
A number which is not a prime number called composite number.
Now we find out the first eight prime numbers
There are ${\text{2, 3, 5, 7, 11, 13, 17 and 19}}$.
These numbers are only divided by one and itself.
Now we want to find the mean value of the first eight prime numbers.
Mean or Average $ = \dfrac{{{\text{sum of all values}}}}{{{\text{number of values}}}}$
Mean ${\text{ = }}\dfrac{{2 + 3 + 5 + 7 + 11 + 13 + 17 + 19}}{{\text{8}}}$
Adding the numerator value we get,
${\text{Mean = }}\dfrac{{77}}{{\text{8}}}$.
Therefore the mean of the first eight prime numbers is $\dfrac{{{\text{77}}}}{{\text{8}}}$ a true statement.

Hence the correct option is $\left( {\text{A}} \right)$

Note: In addition we have to know the following facts:
The number$1$ is neither a composite number nor a prime number
The only even prime number is$2$.
No prime number greater than $5$ ends in $5$.
We also have to know an interesting result called “Fundamental theorem of arithmetic”, states as “every natural number greater than one is either a prime itself or can be factorized as a product of prime numbers”.