Question

Find the mean of first prime numbers?

Answer 1

Hint: Here in this question, we have to find the mean of the first 10 prime numbers. First, we write the 10 prime numbers, the mean means we add all the 10 numbers and then we are going to divide the summation by 10. Hence we can get the required solution for the given question.

Complete step-by-step answer:
In mathematics we have different kinds of numbers namely, natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers.
Natural numbers are defined as counting numbers.
Whole numbers are defined as the counting numbers and along with it 0.
Integers are defined as positive and negative numbers of whole numbers.
Rational numbers are defined as the numbers is in the form of \[\dfrac{p}{q}\]
Irrational numbers are defined as the numbers which are not rational.
Real numbers are defined as the combination of integers and rational numbers.
Here the question contains prime numbers, the prime number is defined as the number which is multiple of 1 but not it is multiple of any other numbers.
Therefore the first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
The formula for the mean is given by
\[mean = \,\dfrac{{sum\,\,of\,\,all\,\,numbers}}{{no.\,\,of\,numbers}}\]
Therefore we have
\[ \Rightarrow mean = \,\dfrac{{2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29}}{{10}}\]
On adding all the terms in the numerator we have
\[ \Rightarrow mean = \,\dfrac{{129}}{{10}}\]
On dividing the number 129 by 10 we have
\[ \Rightarrow mean = \,12.9\]
Therefore the mean of first prime numbers is 12.9

Note: In mathematics we have different kinds of numbers, here while writing the number we choose the numbers which belong to the natural numbers, here we can’t take the numbers from the whole numbers, because the whole numbers has the number 0. So to find the mean we have to use the formula \[mean = \,\dfrac{{sum\,\,of\,\,all\,\,numbers}}{{no.\,\,of\,numbers}}\]