Question

Find the mean of:
(i) the first eight natural numbers
(ii) the first ten odd numbers
(iii) the first seven multiples of 5
(iv) all the factors of 20
(v) all prime numbers between 50 and 80.

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:

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

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

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

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

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

(v) The prime numbers between 50 and 80 are 53, 59, 61, 67, 71, 73 and 79.
Mean of these numbers:

$$\begin{gathered} \frac{53+59+61+67+71+73+79}{7} \\ =\frac{463}{7} \\ =66.14 \end{gathered}$$