Question

Find the arithmetic mean of
(i) the first eight natural numbers
(ii) the first ten odd numbers
(iii) the first five prime numbers
(iv) the first six even numbers
(v) the first seven multiplies of 5
(vi) all the factors of 20

Answer 1

We know:

$\mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{observa}\mathrm{tions}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}$

(i) The first eight natural numbers are 1, 2, 3, 4, 5, 6, 7 and 8.
Mean of these numbers:

$$\begin{gathered} \frac{1+2+3+4+5+6+7+8}{8} \\ =\frac{36}{8} \\ =4.5 \end{gathered}$$

(ii) The first ten odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17 and 19.
Mean of these numbers:

$\frac{1+3+5+7+9+11+13+15+17+19}{10}=\frac{100}{10}=10$

(iii) The first five prime numbers are 2, 3, 5, 7 and 11.
Mean of these numbers:

$$\begin{gathered} \frac{2+3+5+7+11}{5} \\ =\frac{28}{5} \\ =5.6 \end{gathered}$$

(iv) The first six even numbers are 2, 4, 6, 8, 10 and 12.
Mean of these numbers:

$$\begin{gathered} \frac{2+4+6+8+10+12}{6} \\ =\frac{42}{6} \\ =7 \end{gathered}$$

(v) The first seven multiples of 5 are 5, 10, 15, 20, 25, 30 and 35.
Mean of these numbers:

$$\begin{gathered} \frac{5+10+15+20+25+30+35}{7} \\ =\frac{140}{7} \\ =20 \end{gathered}$$

(vi) The factors of 20 are 1, 2, 4, 5, 10 and 20.
Mean of these numbers:

$$\begin{gathered} \frac{1+2+4+5+10+20}{6} \\ =\frac{42}{6} \\ =7 \end{gathered}$$