If the mean of the following observations is 54, find the value of p.

Class	Frequency
0 - 20	7
20 - 40	p
40 - 60	10
60 - 80	9
80 - 100	13

By formula,

Class mark = $\dfrac{\text{Upper limit + Lower limit}}{2}$

By formula,

Mean = $\dfrac{Σfx}{Σf}$

⇒ 54 = $\dfrac{2370 + 30p}{39 + p}$

⇒ 54(39 + p) = 2370 + 30p

⇒ 2106 + 54p = 2370 + 30p

⇒ 54p - 30p = 2370 - 2106

⇒ 24p = 264

⇒ p = $\dfrac{264}{24}$

⇒ p = 11.

Hence, p = 11.