Find the mean of:

Solution:

We know:

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

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

$\frac{1+2+3+4+5+6+7+8}{8}$

$=\frac{36}{8}$

$=4.5$

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

$\frac{5+10+15+20+25+30+35}{7}$

$=\frac{140}{7}$

$=20$

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

$\frac{1+2+4+5+10+20}{6}$

$=\frac{42}{6}$

$=7$

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

$\frac{53+59+61+67+71+73+79}{7}$

$=\frac{463}{7}$

$=66.14$