Question

Find the arithmetic mean of the first 6 natural numbers.

Answer 1

Now first we will list the first 6 natural numbers. Once we have a list of the first 6 natural numbers we will find the sum of these numbers. Now we know that since we have taken 6 numbers to calculate our arithmetic mean, the total number of values is 6. Now the formula to calculate the Arithmetic mean is $\dfrac{\text{Sum of all the values}}{\text{Number of values}}$ . Hence by using this formula we can find the Arithmetic mean of the first 6 natural numbers.

Complete step by step answer:
Now first let us list the first 6 natural numbers.
Natural numbers start with 1.
Hence the first 6 natural numbers are 1, 2, 3, 4, 5 and 6.
Now we want to find the Arithmetic mean of Natural numbers.
Arithmetic mean value is nothing but the average of given data.
Hence let us say we have n numbers ${{x}_{1}},{{x}_{2}},{{x}_{3}}......{{x}_{n}}$ , then the Arithmetic mean of these numbers would be $\dfrac{\sum\limits_{i=1}^{n}{{{x}_{i}}}}{n}=\dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}......+{{x}_{n}}}{n}$ .
Now let us consider the given data.
We 1, 2, 3, 4, 5 and 6.
Now the sum of all these numbers is 1 + 2 + 3 + 4 + 5 + 6 = 21.
Now the total numbers in our data is 6.
Hence the Arithmetic mean of the data is $\dfrac{1+2+3+4+5+6}{6}=\dfrac{21}{6}=3.5$ .

Hence the Arithmetic mean of the given data is 3.5.

Note:
Now if we are calculating the arithmetic mean of terms in AP we can simply calculate it by formula $\dfrac{\text{first term + last term}}{2}$ . Here the first term is 1 and last term is 6. Hence we get the sum of two terms is 7. Now according to this formula we have the arithmetic mean is $\dfrac{7}{2}=3.5$ . Hence we can use this for quick calculation. Just remember this can be used only if terms are in AP.